Tonev, who plays for Lech Poznan, has been followed by Celtic scouts since October.
Tonev has ten caps for Bulgaria, and scored a hat-trick in his side’s 6-0 win against Malta last week.
Tonev was voted Bulgaria’s best young player before making his move to Poland, and is under contract in Poznan for the next two seasons. However, he could be available for between £1.5million and £3m, and is reportedly a target for sides in Italy, Turkey and Germany.