The 25-year-old enjoyed a successful 2022-23 campaign in front of goal, netting 22 goals and providing 12 assists in 50 appearances across all competitions.
However, Gyokeres was unable to steer Coventry to promotion from the Championship, with the Sky Blues suffering a heartbreaking penalty shootout defeat to Luton Town in the playoff final last month.
The Sweden international has just 12 months remaining on his contract and he is expected to seek pastures new this summer amid interest from a host of clubs across Europe.
According to The Mirror, via the Daily Record, Premier League trio Brentford, Wolverhampton Wanderers and newly-promoted Burnley are all interested in signing Gyokeres this summer.
However, the report adds that Scottish Premiership giants Rangers are also in the race for his signature, with head coach Michael Beale said to be an 'admirer' of the £30m-rated striker.
Meanwhile, Portuguese news outlet Record claims that Coventry have received their first offer for Gyokeres from Sporting, with their opening bid worth in the region of €12m (£10.3m) plus €3m (£2.6m) in add-ons.
The report states that Ruben Amorim has identified the Swede as his top target as he looks to strengthen his options in attack ahead of the 2023-24 campaign.
The likes of Everton, Leeds United and Leicester City have also been credited with an interest in Gyokeres, although the striker is unlikely to consider a move to either of the latter two teams following their relegation from the Premier League.
Gyokeres admitted in March that it would be "nice" to play in the Premier League, but he has also refused to ruled out testing himself in other leagues in the future.
Speaking to Swedish news outlet Aftonbladet whilst on international duty, Gyokeres said: "Of course you want to play in the best leagues.
"You have to take [the decision] after the season, now I just try to focus on Coventry... But it is clear that I aim higher.
"Of course it would be nice to play there (the Premier League), but I don't think about it too much. I can play in some other leagues too."
Rangers are on the lookout for a new striker after allowing Alfredo Morelos to run down his contract and leave for free this summer.
Sporting, meanwhile, will soon have the funds to spent on bolstering their squad as they are set to recoup €60m (£51.7m) from the sale of midfielder Manuel Ugarte to Paris Saint-Germain.