Bayern Munich chief executive Karl-Heinz Rummenigge confirmed on Saturday that a deal has been done to take the 30-year-old for Old Trafford.
But former Liverpool defender Carragher is unsure how good the transfer will actually be and also feels the potential exit of goalkeeper David de Gea would mean United losing their best player.
“Great player but at BM (Bayern Munich) he found it difficult to play alongside (Xabi) Alonso be interesting to see how he & (Michael) Carrick works,” he wrote on Twitter.
The comment prompted a response that Carragher was bitter, to which he replied: “You joking? losing your best player (De Gea) & now signing a player past his best I couldn’t be happier!”
He later insisted he was joking, saying: “I don’t actually think he is [past his best] but my afternoon has been a lot more entertaining reading my replies!”
The wider reaction to the signing on Twitter was positive with former England international striker Gary Lineker saying: “Great signing by Manchester United. In @BSchweinsteiger they’ve bought themselves both a brilliant footballer and experience.”
Former United player Danny Higginbotham said: “You can never have enough leaders in a team. @ManUtd had so many for so long but over recent years not enough. Priority I’m sure.