Rushworth spent last season on loan at Coventry, helping Frank Lampard's side win the Championship title and earning a place in the division's Team of the Year after an outstanding campaign between the posts.
According to talkSPORT, Rushworth would prefer to rejoin Coventry City on a permanent basis, viewing it as a better pathway towards a future move to a Champions League club and a possible England call-up than joining Newcastle directly.
Newcastle United are understood to have contacted Rushworth's representatives over a potential deal, and Chronicle Live reports that his services have been offered to the Magpies, who have scouted him in the past.
However, the two parties are yet to hold any formal talks. Brighton remain reluctant sellers, but with only a year left on Rushworth's contract, a decision over his long-term future is likely to be needed soon, whether that means a sale to Newcastle, Coventry or elsewhere.
Coventry have already seen two offers of more than £20m rejected by Brighton, underlining the value the Seagulls place on a goalkeeper who has never made a first-team appearance for the club itself, having instead built his reputation through a series of loan spells at Swansea City, Lincoln City, Walsall, Worthing and Hull City before his breakthrough campaign at Coventry.
Rushworth's representatives are said to be pushing hard for a move to an established Premier League club, which would appear to work in Newcastle's favour, even if the player's personal preference currently leans towards Coventry.
Eddie Howe's side are also continuing to weigh up other goalkeeping options this summer as they look to strengthen their squad following last season's Champions League campaign.
Newcastle have already added Ewen Jaouen for around £18m earlier in the window, and are also weighing up a move for Manchester City's James Trafford, whose price tag of around £30m has so far proven an obstacle.
With Nick Pope potentially attracting interest elsewhere this summer, Newcastle's goalkeeping department could see further change before the window closes, leaving Rushworth as just one option under consideration at St James' Park.
Rushworth's stock has risen considerably over the past year, with the England Under-21 international registering more clean sheets, goal prevention and successful passes than any other goalkeeper in the Championship last season, statistics that have only intensified the interest from both Newcastle United and Coventry City.