Abraham has smashed in seven goals in his last four appearances for Villa, sparking talk of a potential recall to Stamford Bridge.
Chelsea are not exactly blessed with goalscorers, with both Alvaro Morata and Olivier Giroud struggling to hit the back of the net.
But Smith insists that he wants to keep Abraham at Villa Park and he has seen no reason for the striker to go back to his parent club.
“I see no reason not to see him continue here,” he said.
“He’s playing games and he’s scoring goals and that’s what he came he came here for.”
Abraham has gone from strength to strength in a Villa shirt since Smith arrived.
The claret and blues more attacking style seems perfectly suited to the England international forward, who is in wonderful form.
Villa won 3-0 in their last outing against Middlesbrough to push up to the edge of the play offs, with Abraham on the scoresheet again.
Smith’s side are next in action this evening, when they take on West Bromwich Albion.
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