The Gunners will have to battle it out with Chelsea for the in-form striker as both Premier League sides are desperate for a talisman.
Gyokeres has been in top form for Sporting since moving from Coventry last July in a £20million deal.
The 25-year-old has scored 37 goals and 14 assists in 50 games for club and country this season and for Sporting alone he has tallied 22 goals in 24 games.
This has sparked interest from Arsenal who have been on the hunt for a powerful striker this year and Chelsea who have also been analysing his performances closely this season.
The Swedish international goals have helped Sporting take the top spot in the Portuguese league above local rivals Benfica who they defeated in the cup to line up a potential double this term.
Club officials are expected to cash in on Gyokeres by demanding £68m this summer.
AC Milan have also been linked with Gyokeres but the forward is thought to prefer a move to the Premier League after starting his career with Brighton in 2018.
Arsenal have been set on finding a No9 after going a season without a designated striker.
They have been keen on Brentford and England star Ivan Toney and Napoli‘s Victor Osimhen for some time now.
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But The Athletic reporter David Ornstein has confirmed that the Gunners are no longer targeting the pair as Arsenal are more interested in Gyokeres alongside Benjamin Sesko and Evan Ferguson.
Ornstein said: “The likes of Sesko & Gyökeres are well thought of. As is Ferguson but the price Brighton would want & the season he has had so far perhaps makes him less likely at the moment.
“I don’t see it being an Osimhen or Toney. There will be other options too.”