That’s according to Sky Sports, who report that Wycombe and Cambridge United are also interested in the 21-year-old.
It’s believed the Canaries are willing to let the winger leave on loan to continue his development.
Last summer, Jaiyesimi, who is yet to play for the Norwich first team, joined Yeovil in a season-long deal.
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The previous year he had a loan spell at Grimsby.
However, his 2019-20 campaign was cut short in October after he suffered a serious knee injury.
He ruptured an anterior cruciate ligament during a 1-1 draw with MK Dons.
The youngster had scored two goals in 11 games for the then League Two Glovers before his setback.
Pompey have already been to Norwich this summer to boost their League One promotion hopes with the loan signing of defender Sean Raggett.
The Blues have also added winger Ryan Williams to their ranks, following the expiry of his contract at Rotherham.
Meanwhile, Jamal Lowe has consistently been linked with a move away from Fratton Park this summer, with Millwall and Wigan having had bids turned down.