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Young centre-half Diomande joined Sporting from Danish side Midtjylland in January in a deal worth €7.5m, having impressed in Portugal during a loan spell at Mafra in the first-half of the season.
Mikel Arteta has been an admirer since he made that switch with Arsenal approaching his club during the summer transfer window.
It is believed that the Gunners offered Sporting the chance to make a swift and sizeable profit on the Ivory Coast international with a €35m offer which was quickly rejected.
While Arsenal ended their interest for the time being, it is thought they fully intend to return with another offer next summer.
However, new reports indicate that Arsenal are now not alone in their desire to sign Diomande – despite tracking the player for a long time – with up to four clubs monitoring the 19-year-old, who has an €80m release clause in his contract.
Arsenal have already reinforced their defensive options this summer with the signing of Jurrien Timber, who arrived from Ajax in a £40m deal.
But the Netherlands international suffered an anterior cruciate ligament injury on his debut against Nottingham Forest and could possibly be ruled out for the rest of the season.
The north Londoners are unbeaten in their opening four games of the new Premier League campaign and return to action on Sunday with a trip to Everton.