The 29-year-old ex-Tranmere Rovers and Leicester City left-back has not played since rupturing his anterior cruciate ligament just 37 minutes into his debut on loan at Yeovil in January 2014.
"We're providing a base to get himself going," said Crewe boss Steve Davis.
"We certainly know he's good enough," Davis told BBC Radio Stoke.
"I remember him bombing down the wing at Tranmere causing us heaps of problems. He got player of the season there before going to Leicester."
The French-born former Ivory Coast Under-23 international was released in the summer by Leicester, for whom he managed just two League Cup appearances after leaving Tranmere to join the Foxes in July 2013.
But Bakayogo, who still has a home on Merseyside, has been making the short daily journey to Crewe's Reaseheath training ground in a bid to get his career going again.
"We haven't made any decisions either way," said Davis. "He came to us pre-season with a view to us having a look at him, when we were looking for a left-back, before we signed Stephen Kingsley.
"His knee was in poor condition. He'd had a couple of cruciates and had been out for two years. There were doubts about those injuries and we wanted to take a look at him, but he's answering those questions at the moment. He wants to get back playing professional football."
Davis's Crewe still sit bottom of League One, having won just three times in 16 games this season, ahead of Saturday's FA Cup first round date at home to non-league high fliers Eastleigh.

The former England international, 34, has signed on a free transfer after winning friends on and off the field in his three months at the Ricoh Arena.
"He's great to have around the dressing room," said City manager Tony Mowbray.
"The rest of the squad feed off his experience. I'm sure it'll have a positive impact on our young players."
Cole scored a cracking free-kick in a 4-3 win over Barnsley after arriving on 19 October, but has only made seven appearances in total because of injury niggles.
"Our staff have worked hard to build up his fitness and physicality, and we've seen Joe really buy into what we're trying to do here," added Mowbray.
"I only see his performances for the club getting better. He is a fantastic option to have from now until the end of the season."
Cole began his career at West Ham before moving in 2003 to Chelsea, for whom he made 183 league appearances, scoring 28 goals.
After seven years at Stamford Bridge and two Premier League titles, he moved to Liverpool, but had a loan spell with French Ligue 1 side Lille before returning to boyhood club West Ham in 2013.
He made 31 appearances in a one-year spell at Upton Park, scoring five goals, before switching to Villa, for whom he made four starts.
Cole scored 10 goals in 56 international appearances for England.
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Crewe Alexandra are considering whether to offer a deal to on-trial defender Zoumana Bakayogo after almost two injury-hit years out of the game.
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Coventry City's on-loan Aston Villa midfielder Joe Cole has completed a move to the Ricoh Arena on a deal until the end of the season.