Brentford are expected to demand at least £25million for their top scorer, with Villa boss Dean Smith keen on a reunion with the forward he brought to Griffin Park from Exeter in 2017.
Watkins, who was converted to a centre-forward by Thomas Frank ahead of last season, bagged 26 goals across both the regular season and play-off campaign but came up short in Tuesday's final against Fulham.
Brentford are now facing the prospect of having their top stars cherry-picked by Premier League clubs, with top-flight interest in winger Said Benrahma and full-back Rico Henry.
Palace have kept a keen eye on Watkins since last summer as they search to improve an attack which produced just 31 goals across 38 league games last season.
Only bottom-placed Norwich City, with 26, scored fewer goals than Roy Hodgson's side as Wilfried Zaha, Christian Benteke and Andros Townsend struggled with form and fitness.
Jordan Ayew proved a success but is more of a threat from wide, meaning Watkins - who wants a central role - would allow Palace's player of the year to take up his preferred role on the right.
"I feel very comfortable there now," Watkins said recently of his role. "I can’t see myself playing anywhere else to be honest. I feel like I’ve taken to it, I feel very comfortable in this role."
The Eagles are also chasing a deal for QPR's Eberechi Eze, having seen a tentative approach close to £12m knocked back by the Championship club. West Ham are also keen on the 22-year-old, with QPR hoping a bidding war will drive the price up closer to £20m.
A loan for Watford's Spanish winger Gerard Deulofeu following the Hornets' relegation is also an option for Palace, though not a priority as it stands.
Palace are attempting to drag down the average age of their squad, which was the oldest in the Premier League last season and have already brought in 19-year-old full-back Nathan Ferguson on free transfer from West Brom.