Keane played for United at youth level and made one Premier League appearance for the club before sealing a permanent switch to Burnley in 2015. However, his performances at Turf Moor have seen him become the subject of speculation regarding a return to the Red Devils.
Club-mate Ward is unsure about the 24-year-old's rumoured exit from Burnley, but admits that it would pose a problem for the club.
"I haven't heard anything yet, but I wouldn't expect him to," Ward told Goal. "If Michael goes, we're going to have to sign someone because we'll only have three centre-halves."
Fellow Irishman Kevin Long broke into the Burnley back four late in the season and Ward believes that if Keane does leave, the young defender, who recently made his international debut for the Republic of Ireland, could be in line to step up for more regular first team duties.
"Kevin will have a chance," Ward said. "He's shown he's a good player and it's great for him to come in here and it's given him a lot of confidence. It'll be a good battle for him next year.
"He's done great. He's had to wait his chance at club level with the two centre-halves doing so well. As I say, injuries happen in football unfortunately, and he's gotten his chance in the last few games and done really well.
"It's great for him to get a couple of caps here. I'm sure he'll be delighted with that and hopefully a big season ahead for him as well."
Ward also discussed the possibility of Burnley boss Sean Dyche leaving the club amid rumours that Crystal Palace are looking at the 45-year-old as a possible replacement for Sam Allardyce.
"I think you'd have to ask him to be honest," the full-back said.
"Obviously he's done a great job at our place, so we wouldn't want to lose him. He's going to get linked here and there because he's done a good job. It's difficult for us to know, so you'll have to ask him."