As Goal.com exclusively revealed on Monday, the 29-year-old has withdrawn from the Cottagers' pre-season training camp in Switzerland in order to force through a move.
And, with striker Andy Carroll seemingly closing in on an Anfield exit - with West Ham and Newcastle strongly rumoured as potential destinations - Johnson has backed Dempsey to seal a move.
Johnson posted on Twitter: "Andy Carroll on loan to west ham. Looks like its opening up space for my boy @clint_dempsey.
"Dempsey will be a great contribution to Liverpool. #topplayer"
Johnson also later insisted that he meant no disrespect to Fulham supporters with his tweets but reiterated his desire to see a fellow American at a "top" club.
He added: "Fulham is a fantastic club nothing towards the club at all. I read something and him being my mate would be happy if it happened.
"You people are taking this the wrong way. For any American to get the chance to play for a top club like that u wanna see it happen."

Real Madrid have joined the long list of clubs looking to take Moussa Dembele away from Craven Cottage this summer.
Arsenal, Tottenham and Manchester Unite have all been linked with bids for the 25-year-old, who shone for Fulham last season after moving from his role as a second striker to central midfield.
The Belgian has made a huge impression on his team-mates since his £5million move from Dutch side AZ Alkmaar in 2010 and could leave the club for nothing at the end of the season.
The club are reportedly holding out for at least double that fee as Clint Dempsey is also tipped to leave and they will need to increase their attacking options ahead of the start of the Premier League.
But Fulham boss Martin Jol is facing a tough fight to keep the attacking midfielder at the club with the biggest sides in Europe chasing his signature, according to his agent Jan de Visser.
"Real Madrid have contacted us and asked about the possibility of signing Moussa Dembele," De Visser, of management agency Sport International, said in De Telegraaf.
"They are not the first big club who have contacted us this summer for him."
Italian side Roma could gazump Liverpool and sign Clint Dempsey, according to The People.
Dempsey has been tipped to move to Anfield but Fulham are believed to want £10m for the American.
And it is claimed that Roma are now preparing a bid for him - with the £12m fee they received from Liverpool for striker Fabio Borini.
Meanwhile, the Daily Star Sunday suggest Fulham are still trying to sign Vitesse Arnhem defender Alexander Buttner after the apparent collapse of his move to Southampton.
Liverpool risk missing out on Clint Dempsey but are closing in on the signing of Joe Allen, according to the Mirror.
Dempsey has been widely expected to leave Craven Cottage this summer and was left out behind as Fulham traveled to Switzerland for a pre-season training camp in order to push through a move away from the club.
Liverpool have been tracking the American forward all summer but have so far refused to meet the £10m fee Fulham are demanding. This hesitation has alerted Serie A side Roma, who are believed to be ready to meet the Cottagers valuation.
New Reds boss Brendan Rodgers is keen to land the 29-year-old and Dempsey is understood to favour staying in the Premier League, but has not ruled out a move abroad if he doesn’t secure a move to Anfield.
The Mirror claim that Roma manager and former England assistant-manager Franco Baldini is a huge fan of Dempsey and will look to use his contacts at Fulham to negotiate a deal.
There is better news for Liverpool fans though as it looks like Joe Allen will finally seal his move to Merseyside after FSG agreed to sanction a £15m move for Swansea midfielder Joe Allen.
Rodgers has been desperate to sign Allen from his former side since taking the hot-seat at Anfield but has so far been unable to agree a deal after seeing a £12.5m offer rejected by the Welsh side.
However, the owners are now prepared to pay the £15m that will automatically trigger the players release clause, with Allen now free to complete the move after seeing his participation in the Olympics ended on Saturday night when Team GB crashed out to South Korea on penalties.

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