The 22-year-old shot stopper joined Barca in 2010 from the Samuel Eto'o Foundation in Cameroon but left to join the Amsterdam giants in 2015.
Since replacing Jasper Cillessen in Ajax's first-team in 2016, Onana has been the undisputed No.1 and made over 120 appearances for the club.
Barca are said to be on the hunt for a new backup goalkeeper amid reports Cillessen could leave the Catalan side and believe Onana would be a good option to take his place once again.
And the Cameroon international's agent says the Spanish champions have already expressed a desire to get him back.
"That's correct. It's not a secret that Barcelona are interested," Albert Botines told De Telegraaf.
But the Dutch newspaper reports that there are more clubs keen on signing Onana, as Tottenham Hotspur, Arsenal and West Ham have also made their interest known.
Although Barca are reportedly willing to pay around €20 million (£17m, $23m), De Telegraaf claims the Dutch club will hold out for at least €10m more.
Rumours the Catalan side wanted to re-sign the Cameroon international resurfaced late last year, but Ajax's CEO Edwin van der Sar said his side are determined to keep him.
"I think Andre is fantastic," he told Goal in November. "He came to Ajax aged 18 or 19 and the way he developed and the natural attributes that he already had, his speed, his reaction and I think he set himself as a great goalkeeper... I think there are always a lot of rumours about players from Ajax.
We develop great players, not only in Amsterdam but hopefully also in Cape Town and there is interest in a lot of our players, but we like to keep them for as long as possible."
Onana talked about a potential return move back to Spain two years ago, saying: "I would love to come back because La Liga is one of the best leagues in the world. We'll see if I return to Barcelona. If I leave Ajax, it'll be to join an even bigger club."
Onana is currently contracted to Ajax until 2021.