The Spanish agent of Bailly was at United’s training ground on Tuesday to thrash out the terms of a new agreement, likely to tie him to the club until 2022.
Bailly has not played since damaging knee ligaments during a pre-season friendly against Tottenham in Shanghai in July.
It was originally thought that the 25-year-old was facing a minimum of six months out.
But last week Ole Gunnar Solskjaer indicated a return could be on the cards soon.
"I think we can see them coming into training, especially Eric, in the next two to three weeks," the United manager said. "Hopefully he can join the boys and he won't take too long."
After undergoing surgery and months of rehabilitation, Bailly is able to walk without the use of crutches and is targeting a return to light training after the international break.
The ex-Villarreal star, signed for a reported fee of £30million in 2016, penned a four-year contract on his arrival at Old Trafford.
So he would free to leave United in the summer for nothing if the Red Devils don't trigger a two-year extension option in the original deal.
United will want to protect their original investment and get him signed up, particularly as Solskjaer seemed to rate him ahead of Phil Jones prior to his injury.
The emergence of Axel Tuanzebe and the renaissance of Marcos Rojo have made the central defensive positions arguably the most competitive area in the United squad this season and Bailly could become a casualty of that unless he impresses on his long-awaited return.
Some think he also needs to cut out the needless challenges from his game that have led him to spend sustained periods on the sidelines during his Old Trafford career.