The bid, worth around £20m, would have represented a club-record fee for the newly-promoted Coventry, eclipsing the £7.7m they paid for Haji Wright in 2023.
Rushworth, 24, spent last season on loan at Coventry from Brighton, helping Frank Lampard's side win the Championship title and secure promotion to the Premier League.
The England Under-21 international started all 46 league matches during that campaign. He kept 17 clean sheets, the most in the division, and was named the Championship's Player of the Season. Coventry failed to include a buy option in the original loan agreement, meaning they must now negotiate a separate transfer fee with Brighton.
According to reports, Brighton value Rushworth significantly higher than Coventry's opening offer. Rushworth's contract at Brighton runs until the summer of 2027, with the club holding an option to extend that by a further year.
That gives Brighton little pressure to sell at a price they consider below market value. The goalkeeper currently sits behind Bart Verbruggen and Jason Steele in Brighton's pecking order.
Verbruggen, the Netherlands international, is at the World Cup with his country this summer, and any significant change to his situation could shift Brighton's thinking on Rushworth.
For now, though, the rejection leaves Coventry needing to decide whether to return with an improved bid.
Lampard is keen to keep the core of his promoted squad together as Coventry prepare for their first Premier League campaign in 25 years. Rushworth has made clear that his priority this summer is regular first-team football rather than fighting for a place on the bench. Having spent every season since signing for Brighton in 2018/19 out on loan, the goalkeeper is understood to want his next move to be a permanent one.
Coventry remain determined to land their primary summer target and are expected to consider returning with an increased offer in the coming weeks. Whether Brighton's valuation proves a sticking point or simply an opening position in a longer negotiation may become clearer as the transfer window progresses.
For Rushworth, a player who has spent his entire senior career on loan, the outcome of this saga will go a long way to determining where his career goes next.