The Egyptian international, who fell down the pecking order at Boro, sealed a loan move to the Latics until the end of the season.
"There's nothing agreed with Wigan at this stage," Southgate was quoted by Sunday Sun as saying.
"All parties have felt a change for everybody would be good and it's for both the players (Marlon King moved in the opposite direction, under a similar deal) to prove to the two clubs that they’ve got something to add."
Southgate, who used to rely on frontline duo Afonso Alves and Sanli Tuncay, acclaimed Mido, saying the striker's stint at Wigan could help him redeem himself.
"We know his talent. I just felt for him, a different challenge would get more out of him," the 38-year-old tactician said.
"But Mido's still our player, and we have to wait and see what the summer holds."