Cucurella has been linked with a potential move to the Premier League champions with the Spanish international already submitting a formal transfer request to force through an exit from the South Coast.
Talks between the clubs have not progressed in recent weeks with the Seagulls prepared to stand firm over their £50m valuation of the full back.
Pep Guardiola has openly hinted at his interest in bringing Cucurella to Manchester this summer, but Brighton are not interested in lowering their asking price, with the former Getafe full back contracted at the AMEX Stadium until 2026.
According to reports from The Athletic, Brighton have now ended any chance of a possible move, with City missing their deadline of the domestic season start.
Brighton kick off their Premier League campaign at home to Manchester United on August 7.