The 24-year-old has been a prime target for the west African country since bursting onto the scene in 2014-15.
Born to a Ghanaian father and a Liberian mother in Spain's Basque country of Bilbao, the attacker represented the Europeans at U-21 level before earning a senior cap during a friendly against Bosnia and Herzegovina in May. But without a competitive game for La Furia Roja, he remains eligible to switch his international allegiance.
“My parents have met with the Ghana coaching staff and I have received calls," Williams told Reuters.
"I don’t forget where my family came from.
“But on a sporting level, it would be better to play for Spain.
"And I have to be grateful to the place that has given me everything.”
Ghana assistant coach Ibrahim Tanko recently told Goal that his outfit was preparing to make another bid for the striker after unsuccessful attempts.
“I feel very proud to be black, to be Basque, and to play for Athletic,” Williams said.
“There have been very few, but I’m one of them and I’m very happy to be the black guy that represents Athletic.
"This club gave me everything and I try to give them the best of myself.
“Some people are ignorant and think to be black you have to be born in Africa. No. I was born here, I feel Basque, just like my team mates.
“I have African blood but I grew up here, my family has adopted all the Basque customs and so have I.”
This season, Williams has made six La Liga appearances so far, scoring once.