The left-back has fallen down the pecking order in Brendan Rodgers' squad.
Celtic's Emilio Izaguirre
The defender is one of the longest-serving members in the current squad, having made over 200 appearances and winning four league titles since arriving back in 2010.
Last season saw him fall out of favour though, with youngster Kieran Tierney emerging as the first-choice left-back under Ronny Deila.
Kieran Tierney celebrates scoring the first goal for Celtic
He has continued to be first choice under new manager Brendan Rodgers, leading to suggestions that Izaguirre will leave the club this summer.
Indeed, according to the Scottish Sun, he is actively looking for a move away in search of first-team football.
And it appears that he may have an offer in Germany, with Sky Sports reporting that Bundesliga side Werder Bremen are interested in his signature.
Leicester's Riyad Mahrez in action with Celtic's Emilio Izaguirre
It now remains to be seen if the German side will make a firm bid before the end of the transfer window.
It will also be interesting to see if Celtic are willing to accept an offer, with Rodgers likely happy to have him as back-up for Tierney in what is gearing up to be a busy campaign.
Celtic's Emilio Izaguirre misses a penalty