Lampard and Solskjaer both guided their sides into the top four on the final day of the season after wins over Wolves and Leicester respectively.
But Keane believes the Blues boss has performed wonders in his debut season considering he was unable to sign players last summer and lost his best player in Eden Hazard to Real Madrid.
‘Frank’s done a better job, I have to say,’ admitted the former United midfielder on Sky Sports.
‘I expect them to be there or thereabouts, but the way they’ve played, the way Frank comes across, he comes across really well.
‘There’s no nonsense about him, he’s made big decisions, he’s brought a lot of young players in, good players, good quality, but they’ve needed an opportunity, they took it.
‘They finished in the top four and obviously if they can win an FA Cup, great achievement.