New Orleans Pelicans star Davis is one of the most sought-after players in the league as he continues to dazzle despite playing in a struggling team.
It is thought the power forward is wanting to move to a side capable of challenging for the NBA Championship.
The Lakers are in the market for stronger reinforcements as they try to build a team around new addition LeBron James.
However, the Celtics are sixth in the Eastern Conference and have also been mooted to make a move for Davis.
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And Sheridan reckons the Celtics could be leading the race but their pursuit of the 25-year-old could rely on the Pelicans finding a replacement.
'I am told that @AntDavis23 to the @Lakers has been in the works for years,' Sheridan tweeted.
'That does not mean it is a certainty, because @Celtics can give up much, much more.
'And it all depends on whether the @PelicansNBA are able to beef up their roster between now and February.'
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Davis impressed for the Pelicans during the 124-107 defeat against the Celtics last night, scoring 27 points.
However, Lakers reporter Anthony Irwin cannot see Luke Walton's side making a move for Davis this season.
'The nice thing by trading for Davis is that he keeps his bird rights so you can continue to go above the cap to sign him when his free agency hits,' Irwin said on the Locked on Lakers podcast.
'Obviously that would be a tremendous trade but the concern here is whether New Orleans has any reason whatsoever to trade him.
'You're looking at a team that has shown quite a bit of promise early on this season.
'For New Orleans there's just no reason to cut bait with the guy, at least a year before you have to.
'I don't think the Lakers are going to be able to make a trade for Anthony Davis this year.
'I don't think anybody is going to be able to make a trade for Anthony Davis this year, that's just how things have looked so far.'