The 20-year-old former Derby County man is highly-regarded by City boss Pep Guardiola and last season featured in the Premier League against Norwich City and also in the Champions League against Sporting CP.
Delap, the son of former Stoke player Rory, is contracted at the Etihad until 2026 but could look to move in search of regular first team football.
City may be interested in using Delap as part of their attempts to sign Brighton’s full back Marc Cucurella.
Cucurella impressed on his debut Premier League campaign with the Seagulls and Guardiola is keen to secure a deal for his fellow Catalan – who Brighton value at £50m.
Albion have already been quite busy in the summer window and recently signed Paraguay international striker Julio Enciso from Libertad for a reported £10m, as well as finalising a £6m deal for Ivory Coast attacker Simon Adingra.
Check out the latest Premier League transfer speculation below...