The Blues have had a good Premier League campaign. They are currently fourth in the standings with 49 points from 29 games.
Despite this, the club are eyeing an upgrade upfront, considering Nicolas Jackson and Christopher Nkunku have misfired.
Delap has netted only 10 Premier League goals for Ipswich this term, but he has caught the eye with his strong physical presence.
The Blues believe he has immense potential. Manager Enzo Maresca already knows him from his time as Manchester City's academy boss.
Delap has a release clause worth £40 million in his contract. Ipswich could lose his services irrespective of their league status.
Manchester City have a buy-back clause for the same price, and they could yet scupper the Blues' chances of signing Delap.
Delap has also been linked with arch-rivals Manchester United. The 22-year-old could attract more interest in the summer.