Rogers, 23, is currently away on England duty at the World Cup, but speculation surrounding his future is expected to continue throughout the tournament.
Aston Villa boss Unai Emery does not want to lose Rogers this summer, but the weight of any offer is going to dictate whether the club can turn down bids.
Chelsea are looking for a new threat and proven quality in their attack, and sources have told Flashscore that they are very keen on trying to convince him to move to Stamford Bridge.
We reported earlier this week how Alejandro Garnacho could be among the club's departures, and an exit like that would help pave the way for an upgrade signing.
However, it is clear from insiders that Arsenal are also in the picture at this stage and very much admire Rogers.
The player has five years remaining on his current contract - so a valuation towards £100 million is very much a reality from an Aston Villa position.
It remains to be seen whether offers at that level arrive, but Arsenal are certainly being kept informed on how the situation unfolds regarding his future.
Outside of the two London rivals, there is interest at varying levels from Manchester City, Manchester United and Liverpool.
The interest from City could become particularly intriguing once Savinho's future is resolved, as he angles for a transfer to Tottenham Hotspur.
On the surface, Chelsea would not seem well-positioned compared to the other clubs in the race for Rogers. And it is true they would face a big task in winning the battle, which they are aware of.
Chelsea finished 10th in the league last season and do not have European football next season.
However, the club believe they could put forward a competitive financial package and that the ambitious plans under the leadership of new boss Xabi Alonso will hold appeal to top players this summer.
Arsenal are currently regarded as favourites to sign Rogers, but the race for his signature is expected to intensify in the coming weeks.