The former Bastia player has been in Gabon for the Africa Cup of Nations, but his Togo side have exited the competition prematurely.
As a consequence Ayite is heading home and will arrive in London sometime today.
When asked whether a return was too early for him, Slavisa Jokanovic was confident that he would feature.
“No it’s not too early," Jokanovic said.
"He has played three games and he has played at a good enough level during his time away.
"He has no physical problems and will be available for Sunday’s match.”
When asked whether his team were glad to be back on a decent playing surface, having endured difficult services at QPR and Reading, the Serbian chuckled, before composing himself.
“OK, this is the schedule and I am very happy because the draw means that we don’t need to travel so far and it is nice to play at home," he said.
“Our pitch is very good and we are going to try to put the ball on the floor and try to find our identity and our style.
"Hull is generally a big and strong Premier League squad and we are going to try and do what we’ve done better in the past.”
However, Jokanovic was unsure what was behind his side’s penalty woes.
“I cannot explain," he said.
"At this moment it is a problem and we must find a solution.
"We have made a lot of progress this season, but at the moment all we are talking about is penalties.
"I am going to find a solution."
“We are practising penalties a bit more now because we are experiencing some kind of problem, but you can’t replicate match conditions.
"The goal looks smaller and the keeper looks bigger.
"I cannot blame any players, because Chris Martin has scored twice from the spot this season.”
When asked who would take the penalty, Jokanovic replied: “I am going to take the decision and that’s it.
"I am confident that whoever takes it will score.”
Keep up to date with the latest news in west London via the free getwestlondon app
You can even set it to receive push notifications for all the breaking news in your area