Koeman left Southampton to take over at Everton last week and the Saints are currently in the hunt for a replacement.
The report claims that Saints director of football Les Reed has drawn up a shortlist of targets which includes Pereira.
Pereira guided the Yellow Canaries to second place last season and lost the Turkish Cup final to rivals Galatasaray in what turned out to be a trophiless eason.
The Portuguese boss did however, take over a side in transition and still has another two-years remaining on his contract.
The future of Periera remains in doubt with various media reports claiming that he could be on the move but Fenerbahce have backed the experienced manager so far.
Pereira has a lot of experience working abroad having won the Portuguese league title with Porto and the Greek championship with Olympiakos.