According to www.koptalk.org the highly-rated 19-year-old has been watched by Liverpool scouts all season and interest was registered with the player's representative a long time ago.
Carson rejected a contract offered to him by Leeds earlier this month and will be out of contract in the summer.
Liverpool remain favourites to sign the 'keeper even if Leeds reject this initial offer.
If a deal cannot be struck during the transfer window and Carson makes the switch to Anfield in the summer instead, Liverpool would have to pay compensation as the Bosman ruling only applies to players over the age of 24.