Arsenal and Sporting hope to agree a deal for Viktor Gyokeres before the striker is due to report for pre-season training on Friday.
An agreement is yet to be struck between the clubs but negotiations are ongoing.
Standard Sport reported on Sunday how Arsenal’s current proposal of €65million (£56m) plus €15m (£13m) in add-ons is not enough and will need to be increased.
Reports in Portugal state Sporting want more of the €80m (£69m) upfront if they are to sanction the sale of their star striker.
Gyokeres is currently on holiday but the Sweden hitman is due to report for pre-season training with Sporting on Friday.
He has reportedly already agreed personal terms with Arsenal on a five-year contract.
All parties are hoping a fee can be agreed between the clubs before Friday, with Arsenal also starting their pre-season preparations this week.
Mikel Arteta’s squad will be holding a training camp in Spain before next week flying out to Singapore and Hong for a tour.
Arsenal have friendlies against AC Milan, Newcastle and Tottenham while out in the Far East.
The Gunners will then round off their pre-season with matches against Athletic Bilbao and Villarreal in the first week of August.
Arsenal have already begun bolstering their squad for the new season, completing the signings of goalkeeper Kepa Arrizabalaga and midfielder Martin Zubimendi last week.
Brentford captain Christian Norgaard’s move is in its final stages and he is due to join Arsenal this week, with the deal thought to be worth an initial £10m.
As well as a striker, Arsenal want to make further additions before the transfer window closes later this summer.
The club want to add a defender to their ranks and have space in the squad to do so after Takehiro Tomiyasu’s contract was mutually ended a year early last week.
Arsenal would also like to sign a wide player and they are interested in Chelsea winger Noni Madueke. Crystal Palace playmaker Eberechi Eze is also of interest to Arsenal.
It is unclear what new arrivals could mean for Arsenal’s current attackers, with reports in Turkey at the start of this week linking Leandro Trossard with a move to Fenerbahce.
