The Liga outfit are keen to bolster their forward line ahead of the new season as new manager Pablo Machin aims to bring in support for Wissam Ben Yedder.
Machin had been hopeful of completing a move for Chelsea's Michy Batshuayi, but the Blues are reluctant to let the Belgium international leave Stamford Bridge despite their pursuit of a new No. 9 themselves.
He has now turned to Aboubakar, with an offer on the table that is close to the Portuguese champions' valuation of the 26-year-old.
Cameroon international Aboubakar has three years left on his current contract at Estadio do Dragao having scored 26 goals in 43 appearances during the 2017-18 season.
The one potential sticking point should Porto accept Sevilla's bid is likely to be Aboubakar's wage demands.
He currently earns €2.75m-per-year - a salary Sevilla would be unable to match, and as such their own offer would see Aboubakar facing a drop in his wages should he move to Andalucia.
Negotiations have been ongoing since Friday, but with the transfer window not closing in Spain until August 31 the teams have a month to conclude the deal should they require it.
Sevilla's competitive season has already begun, though, having started their Europa League qualifying campaign with a 4-0 win over Ujpest on Thursday.
They begin their Liga season against newly-promoted Rayo Vallecano on August 19 as they aim to improve on their seventh-place finish last term.