With Fulham not retaining his services following their relegation from the Premier League, the Netherlands international is looking for a new club.
The 32-year-old has been strongly linked with a return to the Turkish Super Lig, where he won the title with Besiktas in 2016-17.
It appears that Babel is set for a return to the country, and he has no problems with joining one of his former clubs' main rival, though he says a decision on his future has yet to be made.
"They have the best offer at the moment. I don't have to make a secret of that," he told Algemeen Dagblad when asked about the rumours linking him with the Turkish champions.
"But there are also discussions with other clubs.
"It wouldn't be the first time in football or my own career for things to go differently than expected, so I will just have to wait and see."
Whatever the destination, Babel will be joining his eight club, and it will be the fifth time in his career he has changed teams for a free transfer.
He left Besiktas in December and joined Fulham in January on a short-term deal.
Sporting a colourful haircut, the winger scored five goals in 16 league appearances for the Cottagers, though he couldn't prevent them for returning to the Championship after just one season away.
A big wage bill after a summer of huge spending meant that Fulham have been forced to cut back ahead of their return to England's second tier, and Babel was never likely to remain in west London.
In an interview with the Guardian at the beginning of the year, Babel confessed that "for a lot of different reasons I didn't fulfil my potential."
Turkey appears to offer him a safe haven, having scored 36 goals in the country's top-flight and Galatasaray look set to be the next beneficiaries of his talent and quality.