While it was widely assumed the Mexican would remain with Racing Point Force India, with Esteban Ocon needing to seek an alternative drive pending the arrival of Lance Stroll, over the last week there has been speculation that the Frenchman could stay put and Perez would move on.
Meanwhile, Perez could take a significant amount of sponsors to Woking - even though, according to team boss Zak Brown, the team has already signed more sponsors than any of its rivals.
"We think Sergio's a good racing driver, he's raced here before," Brown told reporters at Monza, when asked if the Mexican was being considered.
"The driver market is fluid," he continued, "you need to keep all your options open. We have a shortlist of about four drivers and we think Sergio deserves to be on that list.
"Ultimately sometimes you are in a position where you can make that decision and some decisions are made for you," he admitted. "Maybe someone's going to announce that's on our list tomorrow morning."
While Brown was giving little away, he appeared to dismiss claims that Lando Norris might make his F1 race debut, suggesting the experience is a major factor in terms of driver choice.
"If you go with young drivers, their lack of experience is something you need to take into account. And also Fernando we hope to have stay with the team in some shape or form."