It is understood one of the clubs to make an offer for the versatile 24-year-old was Wigan, who next season will join the Spireites in League One following their relegation from the Championship.
Blues chief executive Chris Turner said: “The bids have been received in the last seven days and they were both rejected.”
It is understood neither bid came close to Chesterfield’s valuation of the player, who has also been linked with Cardiff and Reading recently.
Clucas joined the Spireites from rivals Mansfield in September 2014 for a fee in the region of 70,000. The Stags will be entitled to a sell-on fee should the former Hereford man move on from the Proact Stadium.
Clucas scored 12 goals in 49 appearances for the Spireites during the 2014-15 season. Although primarily used as a forward, he also impressed when filling in at left-back.