The agent of Grzegorz Sandomierski has told Celtic to up their offer to £2m after seeing two bids blocked by the goalkeeper's club Jagiellonia Bialystok.
The Scottish giants desperately wanted to reinforce their squad before Monday's deadline for the final qualifying round of the UEFA Europa League.
Sandomierski is said to be keen on a move to Celtic Park but the Belgian club Genk also want his services.
His agent Radoslaw Osuch said: "Celtic are closer with their new offer but it is still not good enough for Jagiellonia Bialystok.
"Jagiellonia definitely want to sell him and it's just about who comes in with the best offer.
"I know the people at Celtic very well and I know Grzegorz likes the club. He shares my positive feelings.
"As soon as Celtic match the £2 million asking price, we will be on our way to Scotland. I hope everything turns out well and I feel Celtic want him very much.
"Genk are bidding more so they have a chance as well."