Hulkenberg joined Renault in 2017 after spending three years with Force India alongside Sergio Perez.
The German's current contract expires at the end of the current season, while teammate Daniel Ricciardo, who joined this year, has a deal until the end of the 2020 season.
Renault has often highlighted its desire to promote one of its own junior drivers to the senior team in the coming years, and Abiteboul admits that it is keeping its options open for its 2020 line-up.
"Nico’s contract, the initial term is coming to an end at the end of this year but there is some mechanism of options as has been commented on press," Abiteboul said.
"I'm not going to disclose in the details that can kick in, so it’s maybe that we continue our journey with Nico.
"Frankly, Nico has delivered for the team, clearly, and if you look at where we were when, frankly, Fred [Vasseur] actually was leading that process for us.
"Nico joined us and where we are today, it’s crazy and the change to the team, to the buzz, and clearly the drivers are no stranger to that, it’s not just engineers.
"So I think we need to give credit to that but also we need to look at the options, like everyone is doing, like I’m sure Nico is doing.
"So, it’s a long answer to tell you that things are open for him and for us but there is also an option in place so that we can possibly continue our journey together.
"We will see, we’ll see probably after the summer break will be the right time to sit down, discuss it on the basis of fact and desire also.
Three of Renault's juniors are currently competing in Formula 2, with Jack Aitken Guanyu Zhou and Anthoine Hubert all holding positions inside the top seven in the championship.