Basle's president expects Hakan Yakin to be playing for Celtic or Liverpool next season.
Hakan Yakin will training with Basle on Monday
The Switzerland international impressed against both British clubs during last season's Champions League.
Basle had previously insisted that Yakin would still be their player next term.
But club president Gigi Oeri told the News of the World newspaper: "I've never been in doubt that Hakan would not stay in Basle.
"We spoke for a while at the end of the season and he promised he'd stay unless he received an offer that was too tempting.
"If Liverpool or Celtic make an offer, there's nothing we can do."
Basle would, however, demand a fee of around £1.1m for the playmaker.
Yakin's agent, Ertan Irizik, said: "Hakan will go to Basle's training camp on 30 June and I will hold talks with the British clubs who are interested as soon as possible.
"He'd love to play for Celtic, but I will also negotiate with Liverpool.
"I have spoken to Mr Houllier three times, but at Anfield things take their time.
"Maybe it will turn out to be a case of whichever man moves first."
Celtic manager Martin O'Neill first approached Yakin's agent seven months ago but could make his decisive move as his side return to training this week to prepare for the Champions League qualifiers.
The Glasgow club, along with Liverpool, had also been linked with Turkish international midfielder Yildiray Basturk.
Bayer Leverkusen had claimed that they had accepted an offer from the Uefa Cup finalists and it was now up to the player to decide if he moved to Scotland.
However, Celtic insisted that they had made no offers for any players since the end of the season.