However, recently these stories have gone quiet and now it is rumoured the North London giants are looking at potentially signing Real Sociedad's Mikel Merino and so might not after all pursue a deal for Everton midfielder Onana.
Almost since the day he joined the Blues back in summer 2022 there have been on-off rumours about other Premier League clubs being keen to buy the powerful Belgian ball-winner .
It was clear once last season had finished - with Everton having in the end comfortably survived and avoiding relegation with three weeks to spare despite the points deductions - that players would be sold in the summer.
The Toffees finances were still a mess and there was the looming threat of another PSR breach and deduction to come next season, without significant income being generated before the end of June.
Onana was always going to be the main one of those players available for transfer and indeed he himself seemed ready to move on as soon as possible, judging by reported comments he made.
Arsenal emerged as front-runners for his signature and seemed on the verge of making a concrete move for the 22-year-old not long ago.
Then, as with the stories about Everton's other hugely talented young star Jarrad Branthwaite and links to Manchester United, the rumours about the Gunners and Onana seemed to be petering out before news came last weekend that the Blues were about to sell Lewis Dobbin to Aston Villa.
Dobbin's sale apparently considerably eased PSR pressures on the club - when combined with TV and Premier League income - and so made other player sales less urgent.
Now, it appears as though Arsenal might well move onto Spain's transfer market in search of that additional midfield reinforcement that Mikel Arteta wants.
Even if the Gunners do end their interest in the Belgian star, there will still no doubt be others potentially interested in him with German giants Bayern Munich now being linked with a move for him.
Bayern of course have a new manager in Vincent Kompany, who surprisingly got the job despite overseeing Burnley's relegation from the Premier League last season.
Kompany is a former Belgian international and team captain and so knows Onana well.
With Everton now in a much stronger position than they were a few weeks ago, if he wants to bring his compatriot to Germany the Bundesliga side's boss will have to pay a competitive asking price and surely won't get him on the cheap.