Gary Brown and Stephen Thompson are facing the possibility of a suspension if allegations regarding duo are proven.
The development comes just days after West's Paul Garthwaite was reported to the local football authority for comments he is accused of making on Twitter.
Thompson is also facing claims that he made an offensive comment on Twitter after Saturday's fixture.
A tweet on his timeline on Saturday evening, a reply to one of his followers, said: "w****** mate but we knew it wud happen so just gotta take it on the chin nd we will gav (sic) our day."
It is unclear what offence Brown is alleged to have committed.
Last weekend's match saw West win with an injury-time goal.
Complaints have been made to the Ebac Northern League by supporters regarding the conduct of West's players at a game that many Quakers supporters boycotted in protest at the host club doubling ticket prices, a move that created animosity which shows no sign of abating.
The Northern Echo revealed on Tuesday that a member of the public informed the Durham FA of Garthwaite's comments.
It was a West Auckland club official has lodged a complaint about Brown and Thompson to the local football authority, which will give Quakers seven days to offer a defence.
Durham FA secretary John Topping last night said: "I have received emails from an official of West Auckland Town Football Club that included copies of [Twitter] postings.
"It'll be exactly the same route as the previous case, I'll be writing to Darlington tomorrow and they'll have seven days to respond."
Topping explained in the Echo on Tuesday that a similar offence by a local league player incurred a "two or three game ban".
Tweets on Garthwaite's timeline on Sunday included: "Hate Darlo man f*** them c****" and "hope Spenny win it over them Darlo c****".
In reference to the admission price controversy that led to a boycott by many Darlington supporters, Garthwaite tweeted: "Big thanks to Darlo fans for paying my wages yesterday. Thanks a lot! £££££".
It was accompanied by a picture of an envelope understood to contain his wages from West.
He is now under investigation, but West Auckland manager Peter Dixon has taken matters into his own hands and instructed Garthwaite to delete his Twitter account.
Dixon said: "I have instructed the player to delete his Twitter account and it will remain deleted for the foreseeable future.
"I don't condone what he's done. It was a combination of high spirits and his young friends from Hartlepool. The player will be disciplined internally."
Topping admitted that the situation regarding players making offensive comments is "getting out of hand now, it's crazy".
He added: "I have written to the Northern League today, to tell them that they need to point out to their clubs, whether it's officials or players, that if they're making comments in the public domain which can be seen to be bringing the game into disrepute they will be charged with misconduct.
"No ifs or buts, they will be.
"They may not be professional footballers, but that is irrelevant.
"They're all participants in the Durham County FA and these postings are in the public domain. It doesn't matter that they might be done in personal time."