The club secured it's 20th title in the 2012-13 season to end the final year of Sir Alex Ferguson's reign at Old Trafford, but slipped to seventh last season.
Louis van Gaal has replaced David Moyes at Old Trafford to try to take United back to the top of English football, but former Red Devils captain Keane has warned that could be several seasons away yet.
He told BBC Sport: "It's been a bit better these last few weeks. Clearly they are going to win lots of football matches because they've got lots of goals in their team now. Going forward, the players they have available, amazing.
"But, in terms of winning the bigger prizes again, the Premier League and Champions League, I think that might be a few years down the road yet. Only in a sense that defensively they look to rebuild.
"You can win football matches going forward, with lots of goals, but I think at the back with the lack of experience, and injuries problems at the moment, it will be very hard to win titles."
Van Gaal's side currently sit fourth in the Premier League table.