Jordan, 25, has been the star of the one-day international series against Sri Lanka so far, taking five wickets in Wednesday’s emphatic 10-wicket win at Old Trafford to move England 2-1 ahead.
Swann said: “He looks ready-made for international cricket.
“He looks confident, he looks buoyant and vibrant. He’s a definite candidate for that first 11.”
England will hope to wrap up the one-day series tomorrow at Lord’s ahead of Tuesday’s fifth and final match at Edgbaston.
Alastair Cook’s team then host seven back-to-back Test matches against Sri Lanka and India.