The Mirror says Juve see Delap as a potential successor for Dusan Vlahovic.
With the Serbia centre-forward's contract to expire in 2026, there is talk of Juve selling Vlahovic next summer should new terms not be struck.
Juve chief Cristiano Giuntoli had a scout posted at Portman Road last Friday night to see Delap in action for Ipswich against Manchester United.
Chelsea and United are also monitoring Delap's progress, while former club Manchester City have a buyback clause and negotiated a 20% sell-on option when they sold the striker to Ipswich for £20m in July.
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