BBC Radio Leeds report that it is the latest offer for the 23-year-old international striker.
Leeds director Peter Lorimer said: "We've had lots of bids for Alan, the latest being around £7m from Everton. But we want to get the best offer possible for the club, while Alan's agent has stressed that he wants to go to Old Trafford."
Manchester United have already had two bids of £3.5m and £5.5m for Smith turned down.
Yesterday, Liverpool were reported to have joined the race to sign the forward. The Anfield club are looking for a replacement for Emile Heskey, who joined Birmingham City on Tuesday.