Keane, on loan from the Los Angeles Galaxy, marked his full debut for Villa with two goals, including the winner in a 3-2 win at his former club Wolves.
It enabled McLeish to celebrate his 53rd birthday in positive fashion and Villa have now collected 11 points from their last five away games.
When asked if Keane deserved a bigger stage than the Major Soccer League, McLeish said: "It's one of these things he's chosen to do. It is up to Robbie.
"If he feels he wants to come back to the Premier League, I'm sure there would be some welcoming arms.
"I would like to think we'd be interested. We brought him in. He's paid his dues with that magnificent performance today.
"It was two great strikes. Robbie has done that throughout his career and it was no surprise to see him getting on the scoresheet.
"The winner was spectacular. Not many people shoot from outside the box these days but Keane has done that a few times over the years. They were two sublime strikes."
McLeish praised his side for turning around their fortunes in the second half after Darren Bent's penalty had been cancelled out by goals from Michael Kightly and Dave Edwards.
He said: "I thought the night was going to be ruined but we knew there was still 45 minutes to go.
"That was the key, getting them in at half-time and trying to regroup and showing the character and spirit."
McLeish revealed he had to replace striker Gabriel Agbonlahor at half-time because of illness but his decision to bring on axed left-back Stephen Warnock was tactical.
Wolves have slipped into the bottom three and they finished the game with 10 men after former skipper Karl Henry was sent off for kicking out at Villa winger Marc Albrighton.
In addition, on-loan Arsenal midfielder Emmanuel Frimpong is to have a further assessment of the eye injury suffered during an accidental kick to the head from Villa skipper Stiliyan Petrov.
Frimpong was stretchered off and went to hospital, with an initial examination revealing no head or spinal problems but swelling around the eye.
He returned to the ground and said: "I can't remember too much about it to be honest. I remember heading the ball and, from what I heard, I then got a kick in the face.
"We'll just have to give it a couple of days and wait for it to settle down."
Wolves boss Mick McCarthy had no complaints about Henry's sending-off which means he will have to serve a three-game ban.
He said: "It is a sending-off. It was a foul on Karl from Albrighton and then he is holding onto Karl's leg and the ref doesn't blow.
"He's got hold of his leg and Karl backheels him. Albrighton does roll about as if he has been hit by a steamroller but it is a sending-off.
"For all of that, I'm not excusing him at all because he has backheeled him."