The source told ESPN that doctors have determined that Gore is expected to recover in a few weeks. He was placed on injured reserve after leaving last Sunday's 41-17 loss to the Vikings.
Gore, 35 and a five-time Pro Bowl selection, is in his first season with the Dolphins after signing a one-year contract to play in the city where he starred in college football for the University of Miami.
An unrestricted free agent this offseason, Gore would like to return to the Dolphins if the two sides can work out a deal, a source told ESPN's Cameron Wolfe.
"We'll sit down after the season is over," Dolphins coach Adam Gase said Friday. "We're not in a rush right now.
"... We have not gotten into any of that [returning to the team in 2019]. I know there were times in the season that I could tell he's not ready for that to be even close to being done. We'll sit down and talk about everything and figure it out."
In 14 games this season, he led the Dolphins with 722 rushing yards and an average of 4.6 yards per carry. He also had 12 receptions for 124 yards and a touchdown.
Gore is No. 1 among active players with 14,748 career rushing yards and No. 4 on the all-time list, trailing only Barry Sanders, Walter Payton and Emmitt Smith, who are all in the Pro Football Hall of Fame. He needs just 252 rushing yards to reach the 15,000-yard milestone and 522 to pass Sanders to move into third all-time.
This week's game will be his first missed game since the 2010 season.
"It's disappointing considering the amount of games, the amount of starts that he's had in a row," Gase said Wednesday. "I wish he could've finished this out. He's a special person. He's a special player. I think it's hard to find somebody that's really done anything comparable to him, especially the way football is now and how he's run early in his career.
"To last this long and then to produce the way he has at this age is just something you just probably won't ever see again."
Rookie running back Kalen Ballage is expected to pick up a heavy portion of Gore's workload for the Dolphins. He gained 123 yards on 12 carries in Sunday's loss and scored on a 75-yard touchdown run.