The Bayern Munich midfielder has been linked with a move to Old Trafford, and Cole would welcome his signing.
The German midfielder saw his game time decrease significantly last season, having been a key part of the Bayern side for some time, and that has sparked rumours of a move away from the Allianz Arena.
One of the clubs thought to be interested in his services are Manchester United, per the Daily Star, and their former forward Andy Cole believes he would be an ideal replacement for current midfielder Michael Carrick.
“I like Michael Carrick in the midfield, I’m one of his biggest fans,” he wrote on Kicca.
“He’s just had a few injury problems this season and United have missed him when he is not playing, so it would be nice if somebody could replace him when he’s not there and Schweinsteiger would be ideal.”
Manager Louis van Gaal is looking likely to be busy this summer at Old Trafford as he looks to add quality to his squad ahead of United's return to the Champions League next season.
There is also talk of a potential Premier League title challenge, but success both domestically and in Europe would require an addition of experience to the current side, something Schweinsteiger would certainly bring.
The 30-year-old has won everything in the game, with German league titles and a Champions League at Bayern, as well as the World Cup with Germany, and Cole believes his addition at Old Trafford would be a 'big plus'.
“I think he’s a fantastic player, I really do,” he added.
“He’s a top player who has been at Bayern Munich for a numerous amount of years. He’s a player with great ability and has won everything in the game. If he did decide to come to Manchester united, that would be a big plus.”