That's the opinion of ex-Watford striker Troy Deeney, who believes the Sweden marksman would not win either of the two teams the Premier League.
Gyokeres has established himself as one of Europe's most lethal forwards since swapping Coventry for Sporting Lisbon in 2023.
His first season in Portugal saw him banging in 43 goals in all competitions - firing Sporting to their first league title in three years.
And he has continued his fine form into this campaign, where he has chipped in with 25 goals in all competitions.
He has also found the back of the net ten times for Sweden in 2024, bringing his total tally 60.
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That is 12 more than closest rival Erling Haaland, who has scored 48 goals for Manchester City and Norway.
Having established himself as a goal machine, Gyokeres has been heavily tipped to depart the Estadio Jose Alvalade in 2025.
The 26-year-old boasts a release clause of £85million in his contract, though it is believed that Sporting could allow him to depart for around £60m.
It's reported that United are just one interested party, with a move to Old Trafford to reunite the forward with former boss Ruben Amorim.
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Meanwhile Arsenal are known to be admirers of the ex-Brighton man as Mikel Arteta looks to bring in competition for Kai Havertz.
But both the Red Devils and the Gunners have been warned by Deeney that Gyokeres is not the right player for them.
Speaking to talkSPORT.com, Deeney was asked who out of Arsenal and United would be a better fit for the player.
To which he acknowledged that what he was about to say may seem controversial to some.
He said: "You know when you say something the clip is going to come back in six months.
"I genuinely think he's a good footballer, he works really hard, all of that.
"But I don't think he's a natural finisher.
"And again, everyone is going to pull up his goal record, I get that.
"But I don't think he takes either of those two to winning the Premier League.
"That's just my opinion, and if he did, they'd have already bought him."
And Deeney believes that Gyokeres' output would be nothing like it is in Portugal should he link up with a top-flight team.
The former Birmingham striker likened the player to Darwin Nunez, who scored 34 goals in his final year at Benfica before joining Liverpool in 2022.
In what is his third season in the Premier League, Nunez is yet to score more than 11 league goals.
Discussing the quality in Portugal, he remarked: "It's not the same league (as the English top-flight).
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"And we'll find that out when Gyokeres comes over."
Arsenal fans - and Arteta - got a first-hand look at Gyokeres last month in the club's Champions League meeting at Sporting.
Gyokeres hit the post late in the encounter, but was powerless to stop his side from losing 5-1.
Though he did show his class against Manchester City in early November - banging in a hat-trick in a famous 4-1 victory.
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If Gyokeres continues his hot streak, it's surely only a matter of time before the player tests himself in the Premier League.
And only then can we see whether Deeney is having the last laugh, or is forced to eat humble pie.