The Saints have their sights set on the shot stopper as one of their top transfer targets before the window closes.
Per Fabrizio Romano, the 26-year-old is set for the move as he wants to play regularly.
Ramsdale has been shopped around all summer, but the club have not received the volume of offers they were expecting.
The Saints had been hoping to sign Justin Bijlow from Feyenoord, but he failed his medical.