The Nigerian centre back, who can also play at right back, joined Celtic from Israeli side Ashdod in 2012, and has been a regular at Celtic Park, playing over 130 times for the Bhoys in almost three years at the club.
However, this season, Ambrose has primarily been a backup to first choice centre back pairing Jason Denayer and Virgil van Dijk, though he has featured at right back after injuries to Adam Matthews and Mikael Lustig.
Despite the possibility that van Dijk may move on to a Premier League club this summer and Denayer will return to Manchester City at the end of his loan deal, the Daily Mail believe that Ambrose has decided to quit Celtic and seek first team football elsewhere.
An international regular for Nigeria, Ambrose is likely to attract plenty of interest if he does leave Celtic Park this summer, and it seems that two English clubs are considering bids.
The Daily Mail report that Premier League strugglers Queens Park Rangers and Championship side Fulham are both interested in bringing Ambrose to West London at the end of the season.
A move to England may be appealing to Ambrose, and with QPR reportedly set to lose three centre backs in Rio Ferdinand, Steven Caulker and Richard Dunne, he may be seen as the replacement for one of them, whilst Fulham will be hoping to improve their squad after a poor first season in the Championship.