The Giants had planned to work out McGahee since Friday, according to the source.
Jacobs tweeted about the workout on Monday.
I would like to take this time to thank all the fans who have been behind me all this time.. Ill go (cont) pic.twitter.com/d6Rfkxpqv0
— Brandon Jacobs (@gatorboyrb) September 9, 2013
Jacobs, 31, spent his first seven seasons with the Giants before struggling through an injury-plagued season with the San Francisco 49ers in 2012. San Francisco waived Jacobs in December after the outspoken veteran was suspended for the final three regular-season games reportedly because he used social media to complain about a lack of playing time.
McGahee, who will turn 32 next month, was released by the Denver Broncos in June following a productive 2012 season that was cut short by a significant knee injury. Despite not participating in Denver's voluntary offseason workouts, McGahee insisted that he had no physical restrictions when he was released.
Jacobs rushed for 56 touchdowns in his seven seasons with the Giants and was a key contributor on New York's two Super Bowl-winning teams under coach Tom Coughlin.
If someone's brought in, they'll be welcomed with open arms," guard Chris Snee said Monday. "I obviously have a long history with Brandon and he's a friend. But I obviously have no comment on personnel moves."
McGahee rushed for 731 yards and four touchdowns in 10 games with Denver last season. The two-time Pro Bowler has 8,097 rushing yards and 63 touchdowns over parts of nine seasons with the Broncos, Baltimore Ravens and Buffalo Bills.
If either veteran signs with the Giants, he would provide much-needed depth to a New York backfield that has been beset by injuries and inconsistent play over the past three weeks.
Giants starter David Wilson was benched during Sunday's season-opening loss to the Dallas Cowboys after fumbling twice and struggling in pass protection. Coughlin indicated that Wilson would have a chance to reclaim the starting job.
"Give us a little time to work on this thing," Coughlin said Sunday. "[Wilson] is still very much in our thoughts. He's got to play -- he's a very talented young man.
"But you just can't do that. Every time they touch you, you're going to turn the ball over?"
Receiver Victor Cruz explained Tuesday in an interview with ESPN Radio's "Mike and Mike" what Wilson is doing to change his mindset when it comes to holding onto the football.
"It's just an attention to detail with him. I mean he's got to be able to tuck the ball under his chin," he said. "He's walking around with the football 24/7, around the meeting rooms, around the locker room, even during practice when he's not in that specific play he's gonna have a ball in his hand to just get used to keeping it high and tight and putting it under his chin and really paying attention to detail to it.
"That's the only way you can help with that is to change your mindset from what it used to be, to really locking the football down under his chin and covering it up."
The Giants also will be without veteran running back Andre Brown, who is on temporary injured reserve after suffering a fractured leg in the preseason finale. Brown, who rushed for eight touchdowns last season, will not be eligible to play until Week 9.
"I thought Da'Rel did a good job last night in a role he didn't expect to find himself in," Coughlin said. "But you're always looking to see if there are ways you can improve your roster."
Information from ESPNNewYork.com's Ohm Youngmisuk, ESPN.com's Dan Graziano and The Associated Press was used in this report.