Coleman hopes to bring Liverpool forward Woodburn and Chelsea utility man Ampadu to the Stadium of Light in the next week, according to the Mirror.
Sunderland, who prop up the Championship table, could make five new signings in this transfer window.
Woodburn, 18, has made just one appearance for Liverpool this term.
Jurgen Klopp is open to letting the Wales international leave on loan but Philippe Coutinho’s departure to Barcelona could hold up the move.
Ampadu, 17, joined Chelsea from Exeter in the summer and has made four appearances for the Premier League giants.
Coleman handed both players their international debuts during his spell in charge of Wales.
The Sunderland boss has no money in his transfer kitty so is looking towards the loan market to strengthen his squad.
Ampadu could be the second Chelsea player to make the move to the Black Cats.
Blues defender Jake Clarke-Salter is due to undergo a medical today ahead of a loan until the end of the season.
Clarke-Salter’s switch is expected to be rubber-stamped tomorrow.