The club will be hoping the foursome becomes available, considering Adam McPhee and Nathan Lovett-Murray will miss Sunday's game with suspension.
Fletcher, 33, sat out the Bombers' round seven clash with Port Adelaide with an adductor injury, while McVeigh injured his hamstring in round four and has been missing since.
The experienced pair will line up for fitness tests later in the week, with McVeigh optimistic of a return following his three-match layoff.
Last week, he told the club's website he had "done everything he possibly could" to ensure he was fit for the Bombers' upcoming trip to Sydney.
Lonergan (hamstring) has also not played since round four while Winderlich (groin) missed the Port Adelaide game. Both will be hoping to state their availability for this weekend, after an inexperienced Essendon line-up took to the field against Port Adelaide in round seven.
The Bombers have Adam Ramanauskas (virus) and Kyle Reimers (foot) available for selection, while Damien Peverill (fractured jaw), Scott Lucas (knee) and Scott Gumbleton (knee) are all two to three weeks away from availability.
