"He is a player that we don't want to lose".
Speaking ahead of Wednesday's Champions League qualifier against AEK Athens, the Celtic boss said: "Yes, we have had a few enquiries and there was a confirmed bid by Fulham for him".
Former Manchester City, Bolton and Twente player Boyata was signed by Rodgers' predecessor Ronny Deila in 2015 and the Belgian has made more than a century of appearances for the Scottish side and won 10 senior global caps.
It's unclear whether the player's post referred to the rejected bid from Fulham or was unrelated and just coincidental timing.
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Those performances have alerted a number of clubs all over Europe, but it's the Cottagers who are most keen, with the Press Association claiming that an offer in the region of €15m has been rejected.
Rodgers is also aware that Celtic will have little time to find an adequate replacement for Boyata, with the transfer window shutting in Scotland at the end of the month.
"At this stage it would be pretty hard for us to sell him because there is not a replacement there".
The Belgian defender has only recently returned to training with Celtic after he was given an extended break after his country made it to the semi-finals of the World Cup in Russian Federation.