The 37-year-old spent last season at Championship heavyweights Aston Villa.
However, he packed his bags in the summer with Villa engulfed in financial turmoil.
United boss Jose Mourinho was desperate to sign a new centre-back during the transfer window.
But despite being heavily linked with Harry Maguire and Toby Alderweireld, he failed to sign either.
The Portuguese retains a good relationship with Terry who was his club captain at Chelsea.
talkSPORT presenter Adrian Durham sensationally claimed that United could move for free agent Terry.
He said: “All Manchester United can go with is free agents, John Terry is exactly that so why wouldn’t Manchester United go for John Terry?
“He is better than Rojo, of course he is!
“John Terry would get into the Manchester United team ahead of Smalling, Jones, Rojo, Lindelof.
“Think of the crisis they have got at the back, think about how well Jose Mourinho knows John Terry.
“He is a free agent, it could happen.
“If Jose Mourinho has thought about it, I can see that happening.”
Despite the speculation, The Manchester Evening News claim Mourinho has no plans to sign his former skipper.
Express Sport understands a move back to Villa Park is looking increasingly likely.
New mega-rich owners Nassef Sawiris and Wes Edens are prepared to fund his hefty £60,000-a-week wages.
Villa boss Steve Bruce has found himself short of bodies at the back having failed to land Aberdeen ace Scott McKenna.
Terry spent the summer weighing up a host of lucrative options.
It’s understood cash-rich teams in China and America’s MLS were sniffing around.
He also has broadcasting offers on the table after successful cameos on TV in recent weeks.
Terry has made over 700 professional appearances since making his debut two decades ago.