Bale joined Real Madrid from Tottenham four years ago for a then world record fee of £86million.
The Welshman has cropped up as a Manchester United target with Jose Mourinho keen to add some pace in the wide areas.
Recent reports have suggested that while Bale is being considered, Mourinho would prefer to link up with Chelsea star Willian again at Old Trafford.
But Keown thinks Bale would be a good addition to the Premier League if he were to make a return.
Gareth Bale in Real Madrid training ahead of Champions League final Wed, May 31, 2017
Express Sport brings you the best pictures from Real Madrid's latest training session ahead of the Champions League final against Juventus
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Real Madrid were hard at work in training ahead of the Champions League final
Gareth Bale could be fit enough to start the Champions League final for Real Madrid
I’d be very interested to see Gareth [Bale] come to Manchester United
“I’d be very interested to see Gareth [Bale] come to Manchester United – though I wouldn’t encourage him to leave Real Madrid,” Keown told the Daily Mail.
“On Saturday he could pick up his third Champions League medal.
“He may be accused of not establishing himself as the No 1 at Real Madrid but he is up against Ronaldo, who is one of the greatest to ever play the game.”
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Keown also admitted he would like to see Barcelona duo Lionel Messi and Neymar play in England one day.
Martin Keown would like to see Gareth Bale at Manchester United
He added: “It would really excite the Premier League if Messi or Neymar came to our shores.
“To think you could see some of those players up close.
“Messi is an institution at Barcelona but I wonder if Neymar might be willing to have a new experience in the Premier League.”