However, despite reports in Spain the Hoops have already tabled a £2.4million offer, no formal bid has been made.
Having so far recruited Craig Gordon on a free, and Aleksander Tonev, Jo Inge Berget and Jason Denayer on loans, and with midfielder Wakaso Mubarak awaiting a work permit to join them, Ronny Deila said this week he had to be sure in his stomach about any new signing before he will spend on a permanent transfer.
The Norwegian is convinced Scepovic is the man to lead his line.
However, Celtic face stiff competition for Scepovic with Levante, Almeria and Rayo Vallecano all tracking him, which may spark a bidding war.
The lure of playing in the Champions League, should the Hoops manage to finish the job they started in the play-offs against NK Maribor last night, could be a huge advantage in the race to sign the hit man.
The much-travelled 6ft 1in attacker has played in Belgium for Club Burgge and Israel for Ashdod.
He moved to Gijon last summer, initially on loan from Partizan Belgrade, where he became an instant hit, with 23 goals in 39 appearances in Spain's second division.
In February, Gijon snapped him up on a four-year contract for a bargain £900,000.
Scepovic has experience of European competition, and has eight caps.
Celtic have also been linked with Rennes defender, Jean-Armel Kana-Biyik, but sources at the club have denied any interest in the Cameroon international.