Dr Helmut Marko says he is putting together a "long list" of potential Toro Rosso drivers for 2019.
Pierre Gasly is being promoted to Red Bull Racing, while Brendon Hartley has underperformed this year.
Movement at Toro Rosso
"There needs to be a significant increase (from Hartley) in the last races this season," Marko told Speed Week.
READ: Ticktum not denying Toro Rosso rumour
He said Hartley will not be ousted within 2018, but it means Toro Rosso could have not one but two free seats for 2019.
The candidates are lining up. Red Bull junior Dan Ticktum is struggling to secure the necessary super license, while McLaren says the axed Stoffel Vandoorne should be considered.
Also mentioned as a candidate by Christian Horner is former Red Bull and Toro Rosso driver Daniil Kvyat, while rumours have linked Jean-Eric Vergne and even Robert Kubica and others with the seat.
"There is no shortlist, it's more like a long-list. There are ten names on it," Marko smiled.
But he seemed to rule out Esteban Ocon, noting that one driver "with a Mercedes contract" will "probably not" be considered.
"However, everything is possible," said Marko.