The Sun says Zola is ready to hand on-loan defender Ilunga a two-year deal.
The Congo left-back, 26, has impressed for West Ham since moving from Toulouse in September and he grabbed his first goal for the club in the FA Cup win over Barnsley.
Ilunga’s agent Daniel Striani stated last week his client was growing impatient with the lack of progress over a new deal.
But boss Zola maintains Ilunga is one player he wants to keep.
He said: “Ilunga has been performing fantastically since the beginning and we want to keep him.
“We really trust him and I can tell you he’s not going to leave.”