Former Gunners No.1 Ramsdale has found himself demoted to the bench since the arrival of David Raya in the summer.
The 25-year-old has been restricted to five Premier League appearances and talkSPORT understands he is open to a January exit.
Newcastle and Chelsea are both on the hunt for a new goalkeeper - and Ramsdale has been linked with a move to both clubs.
However, Seaman insists the former Bournemouth star should wait until the summer to see how things develop at the Emirates Stadium.
The iconic Gunners goalkeeper, who made 564 appearances for the club, told talkSPORT Breakfast: "No. I don't want him to leave the club at all.
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"Raya has come in and I think now we're seeing you know why he's in there because with his feet he's brilliant.
"Even last night [in the 2-0 defeat to West Ham], some of the touches that he made were brilliant. It's still 50-50 for me and I'm happy that we've got two really good quality goalkeepers at the club.
"But the main factor that you've got to do is make sure that whoever's not in is happy."
Former England star Seaman admitted Ramsdale will have one eye on Euro 2024 and pushing Jordan Pickford to become Gareth Southgate's No.1.
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"He's also got England to look after as well," Seaman added.
"He's England's No.2, he's pushing for the Euros, so he needs to play.
"But, for me, he doesn't leave in January. Come the end of the season, let's see what happens."