Steven Fletcher has been offered a one-year contract by Celtic after the 33-year-old striker rejected a new deal with Sheffield Wednesday.
But no agreement between the player and the Scottish champions has been reached as yet.
Fletcher, who has 33 caps for Scotland, has also been offered longer-term deals by two of Wednesday's English Championship rivals.
Celtic's offer comes with the option of a further year.
Fletcher, who began his career with Hibernian before moves to Burnley and Wolverhampton Wanderers, spent four years with Wednesday after leaving Sunderland.
He scored 13 goals in 30 appearances last season as Wednesday finished in 16th place.
Celtic manager Neil Lennon has spoken of his desire to strengthen his attacking options amid speculation that French striker Odsonne Edouard is attracting potential suitors.
The 22-year-old started the new Premiership season on Saturday with a hat-trick in a 5-1 win over Hamilton Academical, after which Lennon said it was "pivotal" to his side's hopes of securing a 10th consecutive league title that Edouard remains at the Glasgow club.