Ibrahimovic is a free agent in the summer, with United heavily linked with landing the 34-year-old, particularly if close friend Jose Mourinho takes the Old Trafford hotseat.
The striker has been in great form for PSG, who have already been crowned champions of Ligue 1, with Ibrahimovic netting 27 goals to top the league's scoring charts.
And, according to The Mirror, Keane is convinced the Swede would fit in well at United, who will look to rebuild next season after another disappointing Premier League campaign.
Keane said: "He looks a good character. You’d be happy to play with. He’s a big player for Sweden, we’ll have to keep an eye on him.
“As a player? Really, really good. Seen him recently live, I’ve done a few Champions League games, lot of speculation he might be going to England.
“Talented boy. Looks a bit of a character. Sweden are a very good qualifying team and tournament team.”
"I’d like to be in the trenches with him. Scores goals as well. Big lad, big character. Again, he’s not shy. Pretty confident. One to watch from our point of view.”
The Republic of Ireland are currently preparing for the visit of Switzerland to the Aviva Stadium on Friday, before hosting Slovakia four days later, with both games providing valuable preparation for next summer's European Championships.