While United finished third last season, to secure Champions League qualification, and reached three semi-finals, there are still huge questions over Solskjaer and his team.
Keane believes this will not be good enough for his former teammate this season. The Corkman also believes United will need to finish much closer to Liverpool and Manchester City this season if Solskjaer is to keep his job.
Ole needs to get his hands on a trophy because the honeymoon period is over.
Keane, who is on Sky Sports punditry duty this evening, said: "The remit will be different for Ole this year. Last year it was all about getting top-four.
"It will be higher this year. They need to get closer, the points total can’t be the same. Ole needs to get his hands on a trophy because the honeymoon period is over. The pressure is on now."
United have made a poor start to the season. A nightmare 3-1 defeat to Crystal Palace was followed up with a last-second 3-2 victory over Brighton on Saturday but United gave away a lot of chances once again, something which concerns Keane.
He admitted the signs were "not great" so far.
"Not great. They would have pleased with the result against Brighton, but there’s worrying signs already. It’s early days but they’re giving up chances and goals. The signs aren’t great. The amount of chances they’ve given up is a worry. You would expect them to do better against Palace and Brighton. As a whole, it’s not been great."
