The Hoops get their UEFA Champions League campaign under way next week in Bosnia against FK Sarajevo and are also looking to defend their Scottish Premiership title along with the Betfred Cup and Scottish Cup.
Nice defender Romain Perraud has been linked with a switch to Glasgow - the Toulouse-born defender started his career with Toulouse Fontaines, moving on to US Colomiers in 2009 before joining Nice in 2014. He featured for the Alpes-Maritime club's second-string side and spent time on loan at Paris FC last season.
The 21-year-old is a left-back, and can operate in left midfield if required.
Perraud has been capped at Under-17, Under-17, Under-19 and Under-20 level by France.
Hapoel Be'er Sheva defender Hatem Abd Elhamed is a reported £1.6 million target for the Hoops, says The Sun. The 28-year-old Israeli international, who has had spells at Maccabi Tel Aviv, Charleroi, Ashdod, Dinamo Bucuresti and Gent, is a central defender who can fill in at right-back or in defensive midfield.
He is under contract at the Israeli club until the summer of 2022, and is represented by Dudu Dahan - the Israeli agent who brought Efe Ambrose, Nir Bitton and Beram Kayal to Celtic.
The third player on Celtic's radar is the £700,000-rated Austria-based winger Husein Balic. The 23-year-old plays for St Polten and his impressive displays during the UEFA Under-21 European Championships in Italy earlier this summer have seen him linked with a string of English clubs, according to the Daily Mail.
Balic has 12 months left on his deal at the NV Arena, and if a deal was completed, would provide options for Celtic out wide.