Fredericks, who helped Fulham earn promotion back to the Premier League after beating Aston Villa 1-0 in the Championship play-off final, is out of contract with the Cottagers in June.
However, a contingent of Premier League clubs have been monitoring the defender's situation, including West Ham, Newcastle and Palace, but they all appear set to miss out, with Fredericks suggesting he could be set to sign a contract extension with Fulham.
He said, as quoted by the Evening Standard: "It’s up to the people behind the scenes but I’m sure everyone will want to stay and play at the highest level with Fulham and see what we can achieve.
“Can this club allow me to fulfil my ambitions? Of course. You look at the players we’re attracting, like Aleksandar Mitrovic, we’ve already got Premier League players in the Championship. So I’m sure we’re going to build again and have many years in the Premier League.
“We can achieve a lot. We’re not just going to go there and be a one-season wonder. We want to keep the club in the Premier League for as long as possible. It’s a Premier League team.”