Ramsdale, 27, signed a four-year contract at St Mary’s last summer, in a transfer from Arsenal worth an initial £18million, potentially rising to £24m.
A further £1m was payable if Saints beat relegation from the Premier League, but the South Coast outfit finished bottom of the league in May.
Chairman Solak, lead investor of owners Sport Republic, accepted relegation means Ramsdale likely leaves Saints this summer – at least temporarily.
The five-cap England international knows he must compete in the Premier League in order to make it into the Three Lions squad at the 2026 World Cup.
This week, Solak told the Daily Echo: “We unfortunately are not sure that Ramsdale is going to stay, even though he loves the club.
Saints owner Dragan Solak has offered a glimmer of hope to Aaron Ramsdale’s fans (Image: Stuart Martin)
“He’s a great young man, everybody loves him, but he wants to get his place in the national team and it’s not easy to get there in the Championship.
“He’s even personally looking at all the options of how he would go and come back if we are promoted because he loves the place and he loves the club.
“But generally we understand that he needs to stay within the Premier League level of football to achieve his goals and we will not stop that.
“We want also what is best for him. And there are a couple of other guys, I don’t want to throw names now, who are at a certain place in their careers.
“They probably are not great fit for Southampton. And if Southampton is not a great fit for them, Rasmus Ankersen and I will try to make the best out of it.
“We have WhatsApp groups and exchange a lot of information every day.”
Dragan Solak pictured with Phil Parsons and Rasmus Ankersen (Image: PA)
In theory, Ramsdale could head to the Premier League on loan this summer, with Saints pocketing a small fee, and re-assess his situation next year.
But whether this would prove possible would likely depend on how much cash Saints can raise from the overall sales of their squad this summer.
Ankersen is a board member at St Mary’s but his focus is on Turkish side Goztepe, where he has overseen two successful seasons as president.
Solak says the Dane largely leads the negotiations when selling players, while technical director Johannes Spors leads on recruiting new signings.
Much-maligned Ankersen is seen as the mastermind behind sales such as Romeo Lavia, who was transferred to Chelsea for £53million in August 2023.
Solak added: “Johannes also tells us which guys should leave the club, either because we and the new manager don’t see them as part of the project.
“Or maybe it’s better for them to find a new one. When he talks about players he would like to bring in, the way he explains why, it makes a lot of sense.
“It’s the same thing with the whole composition of the team. I think we got a real benefit in Johannes joining.”