United strolled to a 4-1 win against the Moscovian outfit as they took a giant leap towards the knock-out stages of Europe's elite club competition, with the club's former captain impressed by the huge progress made by Jose Mourinho's side this season.
The Old Trafford legend says he has seen enough from their displays at home and overseas this season to tell him Jose Mourinho's side are capable of winning the biggest prizes.
Keane insists Lukaku's biggest challenge in front of goal for United is yet to come - despite playing and scoring against Real Madrid in the European Super Cup. Whereas over the a year ago or two, you're looking at them and thinking, "They'll win a League Cup" or the so-called lesser trophies.
On the two videos below, Keane hails Manchester United this season and says he expects them to win the Premier League.
"I think the performance can only be good for the team and the players", he stated.
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'He's a good player, a good age, he knows the Premier League, ' said Keane, who played 12 years for United.
Lukaku arrived at Old Trafford from Everton in the summer and has scored ten goals in nine games for Jose Mourinho's side, helping them to second place in the Premier League and two wins from two in the Champions League.
Lukaku has already banged in 10 goals in nine competitive games for the club and he was in lethal form against CSKA Moscow. "Big, strong boy. Speaks well, comes across well, and seems like a decent character".
"Realistically, I don't see United going as far as the semi-finals this season".
"You need a star player and Man United have got players that could become that, but we need to find out who that will be and if they can reach that level".
"We have started competitions strong in August and September and have now just one more game, a hard one".