Having recently sold Jack Rodwell to Manchester City for a fee which could rise to as much as £15m, Moyes is keen to bolster his midfield options. And Adam, a Scotland international, fits the bill.
He could be available for as little as £5m. Moyes' brother, Kenny, is also Adam's agent.
Should Adam seal a switch to Everton, then he'd become the first player to cross the Mersey divide since Gary Ablett in 1992.
Charlie Adam was bought by Kenny Dalglish after a good season with Blackpool; Adam almost secured promotion for The Tangerines through his performances. He was not the lone performing figure within Ian Holloway's setup, but he was certainly one of the most influential.
At Liverpool, however, things were a bit different.
Adam did not need to concentrate on his defensive duties with Blackpool. At Liverpool, he needed to but just could not adapt. People who thought his red card against Spurs was a one-off incident might have reassessed that opinion after seeing how bad the Scot's tackling actually was further on in the season.
Adam did rack up some good assists but still was considered to be a liability. Even in preseason, Rodgers preferred Jonjo Shelvey to Charlie Adam, perhaps because Shelvey is more mobile. Even if Joe Allen hadn't been signed, Adam would not have started many games.
He would not have been sold just to have something instead of nothing with regards to cover for the midfield.
The former Blackpool player being left-footed is something of an advantage, as he gives balance to the side. I think this is the reason why Rodgers is courting Nuri Sahin of Real Madrid (h/t Express.co.uk). Sahin is very similar to Adam, only younger, more mobile and has better statistics playing for a team like Borussia Dortmund.
The price mentioned in the report is £5 million. I don't see any way Liverpool will get anything more than that for Adam.
I personally wanted Adam to have a good career at Liverpool, but sadly he did not play anything like what he did for the Seasiders.
Neither his magnificent delivery nor his "£10 million" corners were anywhere to be seen. Liverpool created a huge number of corners last season, but sadly no one could find the right delivery. Adam let the pressure of being at a big club get to him. That is one thing that separates the good from the great.
It is not only about ability but mettle, as well.
Charlie Adam may not necessarily go to the Toffees as this rumor suggests, but his days entertaining the Kop are certainly numbered.
Here is wishing the Scotsman best of luck with his footballing future.