The 23-year-old, who is also reportedly interesting a number of European clubs, is regarded as one of the brightest prospects in Bulgaria.
"It's an honour to know Celtic are interested in me. They have a big history and their performance in Europe this year has shown they are ready to create some new history," Tonev told the Daily Record.
"Last summer there were Italian teams interested and even though Serie A is one of the top leagues it's important for me I consistently play Champions League football.
"Celtic is somewhere I could achieve that. I just concentrate on playing. Hopefully a move can be organised this summer."
Tonev still has two years remaining on his current deal.