Clarke is currently the top goalscorer in League One having found the net 15 times this season, while he has also been on target three times during Coventry's FA Cup run to the fourth round.
The 28-year-old signed a two-and-a-half-year contract with the Sky Blues last January and, with 18 months of that deal still remaining, the midlands club insist they will only let him leave for the right price - with Clarke linked to a return to former club and League One rivals Wolves.
Coventry development director Steve Waggott on Monday said: "I have this morning received a formal transfer request from Leon Clarke. There had been indications over the weekend that this would happen but I was only formally notified this morning after he arrived at the training ground.
"Of course, it's deeply disappointing when a player expresses a desire to leave the club in this way - especially when he has become such a firm favourite with supporters because of performances over the past 12 months.
"That said, when he still has a year-and-a-half left on his contract, we are in a position where we will only let him leave if the deal is right for Coventry City Football Club.
"That means securing the kind of deal that will allow Steven Pressley to strengthen his squad should Leon go."
Clarke spent the first half of last season on loan at Scunthorpe from then parent club Charlton, scoring 11 goals in 15 games.
He then briefly joined Coventry on loan from the Addicks before tying up a permanent deal, going on to score 10 goals for City between January and March before his campaign was cut short by injury.
Wolverhampton-born Clarke started his career with Wanderers before going on to enjoy spells with Sheffield Wednesday, QPR, Swindon, Charlton and Coventry as well as a host of loan moves.