Amid the McLaren-Honda crisis, Spaniard Alonso is clearly on the market and rumours have linked him with a return to Renault, where he won his two titles over a decade ago.
“I know you want to know something about Alonso and Renault,” Abiteboul told the Spanish sports newspaper Marca.
“I can only say that firstly Fernando is a world champion, we understand that he knows his time is running out, but we have to see what he wants to do with his life.
“So first he has to know what he wants himself. Does he still want to continue in formula one? Is he still passionate about the sport?
“Communication has never been cut, there has always been a kind of loyalty, but there is no need for him to wait for our team — he knows where we are,” Abiteboul added.
“Right now we are in full development and we want to focus on carrying out this work with the drivers we have, Jolyon and Nico,” he said.
After Barcelona, Alonso will skip Monaco to do the Indy 500.
Abiteboul said: “Being at Indy instead of Monaco proves that he wants to see what’s outside of F1 and find the answer if he still loves F1. It is the first question to be answered.
“There will be time to talk but I don’t want to feed rumours,” he insisted. “Alonso is always a member of our family, but everyone has to make his living as well.”