AlphaTauri is in talks with several sponsors with a 2024 name change on the horizon.
The clothes brand partnered with Red Bull to take over the naming rights of the champions' sister team which was previously known as Toro Rosso.
Tost, who will leave the team at the end of the year, has ruled out a return to Toro Rosso with the team aiming for a big sponsorship to take over naming rights and funding.
The team will also move to the UK from Faenza to be closer to the senior outfit and hopefully improve on-track performances.
AlphaTauri will move to the UK in 2024 to be closer to Red Bull
"At this time of year, all teams negotiate with sponsors," Tost said, as quoted by Auto Hebdo.
"Of course, we have several negotiations underway, and having a title sponsor can be interesting.
"We will see what the negotiations bring in the coming months. We speak with several companies, there is a big interest in AlphaTauri, but nothing is confirmed or signed until now.
"That probably won't happen in the next few days. We rather speak in months."