The Cats have been forced to deal with early issues within their midfield pack to start the season, with clearances and contested numbers significantly down from their premiership-winning 2022 campaign.
Parish, who re-signed with the Bombers on a two-year deal midway through 2021, is off-contract this season and is sure to be in the sights of rival clubs.
While Geelong were able to bolster their list last year, the Kardinia Park club could potentially move on Essendon's star onballer at the end of this season.
A product out of Winchelsea - a country town west of Geelong - Parish would not only suit the Cats' needs, but would also move closer to home if he was to consider a switch to the hoops.
Expected to hold off on a decision until later in the year, the gun Bomber is said to begin gaining external interest in his services.
Speaking on Triple M, reporter Tom Browne revealed the Cats have been linked to Parish and could look to lure the midfielder closer to his home town.
"Just a whisper, just some word that perhaps (Geelong) would be looking at Darcy Parish at the sharp end of the season in terms of contract talks," Brown said.
"(Parish) has a Winchelsea background, a Geelong Falcons background, suits their modus operandi down there. They could do with an accumulator in the form of Parish.
"I don't think Geelong would be in a position to party top dollar for him. I'm not saying they'll get him, but he's the sort of guy they'll look at at the end of the year."
Should Parish exercise his rights as a free agent, the Bombers would likely acquire strong draft capital in return for his departure, with his standing in the game and likely salary demands potentially seeing Essendon receive a first-round selection.
An integral part of their midfielder and currently leading the league for disposals after three rounds, Essendon will be wanting to lock away Parish for the coming seasons.
The Bombers were already able to secure their top retention priority this year with the extension of forward Peter Wright ahead of Round 1, with Parish seen to be among the next rung of re-signing targets at Tullamarine.