It’s understood the ex-England striker, released by West Ham at the end of the season, is attracting strong interest from the Middle East.
The hitman, who started his career at Chelsea, is considering his options and is aware there could also be renewed interest from England.
However, first team coach John Kennedy is still hopeful the free agent can be persuaded to come to Parkhead.
“It was difficult to judge him properly. It’s now been left with the manager, Peter Lawwell and Carlton’s representatives.
“The manager spoke to him before he left and said he’d be in touch. Peter was to speak to his representatives to see what the deal was going to be.
“It obviously has to be something that is good for both parties if a deal is to be done.”
Celtic expect Croatian defender Jozo Simunovic to recover from an ankle injury in time for Thursday night’s Europa League group match against Fenerbahce in Glasgow.
Kennedy added: “With the calibre of team and players on show, it will have a Champions League feel to it. It’s two big clubs and it’ll be similar to Champions League standard.”