Musselwhite returned for a second spell at Glanford Park in the summer of 2004, helping the side win to the runners-up spot in League Two.
But he lost his No.1 spot to Tommy Evans midway through this season, and the 37-year-old is not expected to be offered terms to stay on.
Eastleigh manager Paul Doswell hopes to entice the keeper back south, and has held informal talks with the player.
He told the Scunthorpe Telegraph: "We have spoken to him two or three times and he is due to come down today or tomorrow.
"We will be trying to convince Paul to come here. He would be a major coup for us.
"He is a player we have been watching for some time and we will be very pleased if we can get him.