Ba, who has been capped 10 times by his country, earns around £30,000 per week, but is believed to be keen to remain in the Premier League and would fit the bill, style-wise, for Moyes’ side.
He does, however, have a chequered injury past. A long-standing knee injury scuppered a potential move to Stoke earlier this year, and Moyes will be wary of adding an injury-prone player to his squad.
First-choice Louis Saha has struggled to stay fit throughout his Goodison career, and neither Jermaine Beckford nor Victor Anichebe - who scored for Nigeria in a 4-1 friendly win against Argentina on Wednesday night - have proven themselves on a consistent basis.
Meanwhile, teenage midfielder James Wallace could be set for a loan switch to Sheffield Wednesday.
The 19-year-old spent the last three months of last season at League Two side Stockport County, and this week signed a new one-year contract at Goodison Park.
Wednesday boss Gary Megson is keen to add the England under-20 international to his squad, as he looks to secure the Owls promotion from League One.
Wallace himself, however, is focusing only on Everton.
“I am delighted to sign a new deal at the Club,” he said. “I am made up it is sorted and I am just looking forward to pre-season.”
Elsewhere, highly-rated duo John Lundstram and Tyias Browning have signed two-year professional contracts.