Scott Brown and Kevin Thomson's agent claims Hibernian have rejected a £4.25million bid from Celtic for the duo.
The Hibs pair are hoping to secure moves away from Easter Road after a contract dispute with the club.
A number of clubs including Celtic and Rangers have expressed an interest in the midfield pair, but Celtic were keen to steal a march on their rivals by luring them to Parkhead.
Both players have also expressed an interest in making the switch to Celtic, but Hibernian are determined to keep hold of the pair.
The duo's agent Willie McKay claims Celtic's fresh offer has been rejected by Hibs and he believes the Scottish champions may drop their interest in both players and look elsewhere.
"Celtic upped their previous offer today, going up to £4.25million - but Hibs knocked it back," McKay told the Scottish Daily Mail.
"Kevin and Scott are a bit upset. At a time when Celtic can go into the loan market and get full internationals through just paying their wages, I think they will just walk away from this.
"I believe it is a great offer, especially as Celtic were willing to wait until the end of the season to get them.
"That would have allowed both players to stay at Hibs and play in the CIS Cup and the Scottish Cup."