Ajax are yet to respond to the offer amid their need for defensive cover having recently lost Jurrien Timber to Arsenal.
Despite only joining Ajax from Rangers last summer, Bassey has been linked with a move away from the Eredivisie giants after falling out of favour towards the back end of last season.
However, the 23-year-old is keen to get his place in the starting XI back under the tutelage of new Ajax boss Maurice Steijn.
“Of course, I trained all summer long – you want to come back in the best shape,” Bassey told Ajax TV shortly after reporting for pre-season duty.
“We have a new coach, so a good start is important. Hopefully, I can score some bonus points. I’ve been working hard, so it should work out.
“I’m happy to be back and looking forward to the new season – my intention was to return in peak condition.
“With a new coach at the helm, I’m determined to kick off on a positive note and hopefully make a significant impact. I’ve put in the hard work, and I’m confident it will pay off.”
While Fulham have already stepped up their interest in Bassey with an official bid, they are not the only club keen on the Nigerian who is also wanted by Brighton & Hove Albion.
However, with Brighton closing in on the acquisition of Igor Julio from Fiorentina, Fulham could be set for a free run at Bassey.
Fulham are keen to add defensive reinforcements this summer and have already had a bid for Benfica’s Felipe Morato rejected.