The club’s leading goalscorer from last season was the subject of a bid from the Ibrox side last week, thought to be in the region of £200,000.
Levein described the offer as “disappointing” when he spoke the media following Hearts’ 5-0 victory over Inverness CT in the Betfred Cup.
Lafferty was a second half substitute in the match, fuelling speculation that he’d soon be on his way out of Hearts with reports of the Northern Irishman seeking to force the club’s hand.
However, the Evening News understands that the situation remains amicable between player and club and no transfer request has been made by the 30-year-old.
Lafferty netted 19 goals last season and Hearts are understandably keen to hold on to the fans’ favourite. He has less than a year remaining on his contract.