FOXBOROUGH, Mass. — For Mike Gillislee, it was a case of one-stop shopping.

The veteran running back’s lone visit during his time on the market as an NFL free agent this year was a stop at Gillette Stadium well into the process.

“It was a surprise because it was getting to a point where no team came at me and it was coming to an end where I had to sign a tender,” Gillislee said during a break from the Patriots’ off-season conditioning program at Gillette Stadium on Tuesday. “But New England came and it all worked out for me.”

It all worked out with a two-year, $6.4 million offer sheet the Bills chose not to match, leading to the restricted free agent’s relocation to Foxborough with Buffalo receiving a fifth-round pick in the recent NFL draft from the Patriots as compensation.

Thus, Gillislee became the latest move in a changing backfield in New England. Former Cincinnati running back Rex Burkhead was added to the mix, while LeGarrette Blount – who enjoyed a career year with 1,161 yards rushing and a league-leading 18 touchdowns in 2016 – remains out on the open market as an unrestricted free agent.

“LeGarrette Blount, he’s always been one of my favorite running backs in terms of his physicality and what he brings to the table,” said Gillislee. “It’s something I bring to the table, but I wouldn’t compare myself to him. I’m just here to better this football team and continue winning games.”

Even with Blount’s absence, and with holdovers James White, Dion Lewis, D.J. Foster and Brandon Bolden still in the picture, the additions of Burkhead and Gillislee could make for one crowded backfield.

“That’s everywhere,” Gillislee said of the competition he’ll face here. “Every team has competition. You can never get comfortable in this league. We’ve got a great group of guys here and I just look forward to competing with them.”

Although second to LeSean McCoy in Buffalo last season, Gillislee’s 5.7 yards per carry (101 carries for 577 yards and eight TDs) led the league.

A fifth-round pick of the Dolphins out of the University of Florida in 2013, the 5-foot-11, 208-pound Gillislee has averaged 5.6 yards per carry over his career, gaining 865 yards and scoring 11 touchdowns on 154 carries in 23 games with Miami (one season) and Buffalo (two). He’s also caught 15 passes for 79 yards and one TD.

Gillislee enjoyed one of the most productive days of his career against the Patriots last Oct. 30, gaining 85 yards and scoring a touchdown on 12 carries and catching three passes for 9 yards in the Bills’ 41-25 loss. In his next-to-last game with the Bills, he gained 91 yards on 11 carries in a 34-31 loss to the Dolphins.

At this point, though, Gillislee isn’t looking back at past opportunities he might have had, only to those that might lie ahead.

“It’s all about opportunities,” said Gillislee, “and I was blessed to come here and get another opportunity, so I look forward to that.”

New England star cornerback Malcolm Butler has returned to Gillette Stadium to participate in offseason workouts with his teammates this week, according to ESPN.

Butler had not been participating in the voluntary workouts prior to the NFL draft. Butler is still on the roster, and it seems as though he will not be traded. A player-for-player swap is always possible, but those moves are rare in the NFL.

Butler likely will play the 2017 season on his first-round tender – worth $3.91 million – before becoming an unrestricted free agent next spring.

“Now that he knows he is with the Pats after the draft, he plans to be back to business as usual and working out to get ready,” a source close to Butler said this past weekend.

Butler will team with Stephon Gilmore to form one of the NFL’s best cornerback duos.

BILLS: Brian Gaine, the Texans’ director of player personnel, has been given permission to interview for the Buffalo Bills’ general manager’s job, according to the Houston Chronicle.

Gaine was a tight end at the University of Maine, graduating from the school in 1995. A native of Pearl River, New York, he is interviewing for the job that opened when the Bills fired Doug Whaley.

Gaine was hired by Houston General Manager Rick Smith in 2014 as director of college scouting. He was promoted to director of player personnel and has earned a reputation as one of the best scouts in the league.

SAINTS: Adrian Peterson scoffs at the notion that a decade in the NFL and a pair of knee injuries have somehow left him a worn-down, less effective version of his former dominant self.

“It’s kind of crazy to hear people even comment on how many years I have left and compare me to other running backs when I’m just my own individual,” said Peterson, who signed with New Orleans last week.

“There’s a different mindset, work ethic, body type. This is one thing that I really just dislike about the NFL and kind of how a lot of people try to put guys in a box – especially running backs after that 30 (years old) mark. … They make it seem like guys are going downhill and that’s not necessarily the case – and so in my mind, I feel like I have a lot of years left.”

The Saints are hoping the 32-year-old Peterson, who missed most of last season because of a meniscal tear, has at least one good year left. The Saints signed him to a two-year, $7 million contract for which only the first year is guaranteed.

JETS: Josh McCown has every intention of being the starting quarterback this season.

Whether that means 16 games, eight or just one, the 37-year-old veteran believes he can still be plenty productive. But if McCown ends up being the backup – and an invaluable mentor – to Christian Hackenberg or Bryce Petty, he’s OK with that, too.

“It’s a full competition between the three of us,” McCown said Wednesday.

PANTHERS: Carolina claimed defensive end Zach Moore off waivers from the San Francisco 49ers. The 6-foot-6, 280-pound Moore was a 2014 sixth-round draft choice of the Patriots.

CARDINALS: Arizona signed center/guard Tony Bergstrom to a one-year contract.