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Any prospective deal could be helped along by their new sporting director Andrea Berta, whose appointment was confirmed on Sunday, as the Italian is understood to be a big fan.
Gyokeres’ name appears on Arsenal's shortlist of targets along with Newcastle United frontman Alexander Isak and RB Leipzig starlet Benjamin Sesko, while Eintracht Frankfurt’s Hugo Ekitike has been linked.
Mikel Arteta has already missed out on signing Isak once, as the Spaniard wanted him prior to his move to Newcastle from Real Sociedad in 2022.
He helped them lift the Primeira Liga last year under Ruben Amorim - now in charge of Manchester United - and has 30 goals in 26 games this term.
Amorim has been consistently linked with a reunion with Gyokeres at Old Trafford, but Arsenal’s pulling power of Champions League football could convince him.
Chelsea have also been rumoured to be monitoring his situation, but the Blues' are focused on signing younger players with high potential.
The change of course could represent good news for Liverpool, who could find themselves locked in a battle with Arsenal to capture Isak as Arne Slot considers selling Darwin Nunez.
The Uruguayan has been subject of interest from Saudi Arabian clubs and his departure could fund a move for Isak, with the Reds prepared to splash out this summer to reinforce the Dutchman's squad.
A move for Isak could well depend on whether Newcastle qualify for the Champions League next season.
The 24-year-old has said he is happy to stay on Tyneside, but a bid in excess of £100m from likely champions Liverpool could test their resolve.
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