The Parkhead club are also running the rule over Club Brugge's Nigerian striker Joseph Akpala. And the Celtic boss is also keen to bring in Rosenburg midfielder Markus Henriksen to bolster their assault on Europe.
West Brom player Cox, who can play up front or out wide, has been linked with a move to Parkhead during the summer months.
Meanwhile, Celtic have held further talks with Fraser Forster's agent about the English goalie moving to the club permanently.
The 24-year-old is still under contract at Newcastle, but the clubs have agreed a fee of around £2million.
Lennon this week expressed confidence Forster would see his future at the club.
The Hoops gaffer is also confident top scorer Gary Hooper will put pen to paper on a new contract despite speculation linking him with a move to Southampton again. It had been reported his wage demands were too great for Celtic.