The Uruguayan joined the Scottish champions on a permanent basis on the final day of the last transfer window, but there was not option for Celtic to keep him permanently included in the deal.
AC Milan valued Laxalt at £9m in October, but are keen to offload him and are open to dropping his price tag when his loan spell in Glasgow ends.
It remains to be seen if Celtic might want to try to sign Laxalt on a permanent basis, but boss Neil Lennon has handed the left-sided player regular minutes.
Laxalt has been trusted by Lennon in the left-back role and was again in action last weekend when Celtic took on rivals Rangers in the Glasgow derby.
With AC Milan willing to lower his asking price, Laxalt may become an obtainable target for a number of clubs when his loan at Celtic has run its course.
He featured heavily for Celtic during their Europa League campaign and faced parent club AC Milan in both group stage meetings, though ended on the losing side on each occasion.
Laxalt is under contract at the San Siro until the summer of 2022.