The Demons are targeting Collingwood pair Dawes and Sharrod Wellingham during the three-week trade window.
Wellingham has nominated West Coast as his preferred destination and Harrington said there was a 'competitive market' for the gun midfielder.
Harrington said the Demons were eager to bring Dawes to the club, but admitted little progress had been made on Monday.
"They (Collingwood) are still saying that we need to do a deal that satisfies them quite rightly," he said.
"But we are keen to progress that with player and club so we're going to push forward as best we can.
"I wouldn't say we're any closer than what we were last Friday."
Harrington said it was 'unlikely' that Melbourne would give up an early pick for Dawes, who could join the Demons even if they cannot get Wellingham.
After securing Jack Viney son of Melbourne great Todd with pick 26 the Demons are also chasing 17-year-old Jesse Hogan.
Harrington said Melbourne were willing to give up pick three to bring Hogan to the club.
"We rate him extremely highly," he said.
"We think he's going to be someone who we can really develop a team around and with. That's a big statement for a 17-year-old but he's impressed us no end, on and off the field."
Harrington said the club would be doing 'handstands' if they managed to get Hogan with pick three and Viney at 26.
In other trade news, Sydney and Adelaide made a 'courtesy start' to discussions about Crows forward Kurt Tippett, Swans chief executive Andrew Ireland said.
Port Adelaide football manager Peter Rohde said Jared Rivers was 'unlikely' to join the Power with the defender 'pretty keen' to stay in Melbourne.He said the Power were looking at key defenders and had some interest in Carlton's Jordan Russell, while they are not expecting to lose any other players.