The midfielder left Derby County for the Clarets this week.
Keane said: "I have always liked Jeff. He has matured over the last year or two. He's probably played better in international football than he has at club level, maybe.
"He had a few injuries last year, to be fair, for Derby. He missed a bit of the run-in with them, but I'm not surprised Jeff has got his move.
"He's gone to a good club in Burnley and from a selfish point of view, we obviously want all our players playing at the highest level, in the Premier league or abroad as one or two have tried. I think its good news all around."