Senior players like Rui Patrício and William Carvalho are supposedly pushing for a move away from Lisbon this summer and Arsenal submitted a €30m offer in an attempt to lure Martins to the Premier League.
The club's first offer was rejected outright and that decision is claimed to have left Martins furious with Sporting, prompting Arsenal to launch a second offer for the unsettled forward.
Portuguese outlet A Bola have run with a frontpage story claiming that Arsenal are 'insisting' on signing Martins this summer, with their second offer matching the €30m that was rejected last week.
A Bola say Arsenal insisting on Gelson Martins and have submitted a second offer which was also rejected by Sporting. pic.twitter.com/TchrzdI7XL
The club's chief negotiators, Raul Sanllehi and Sven Mislintat, are hoping that Martins' frustration at being denied a transfer to the Emirates will help force a move through.
There are also concerns from Sporting that the attack on their training complex could give the 23-year-old winger grounds to have his contract at the Estádio José Alvalade terminated, which would leave him available to join Arsenal on a free transfer.
Martins, who has spent his entire club career with Sporting, scored 8 goals and bagged 9 assists in 31 league appearances last season. He also scored a goal and had two assists during the Champions League last term, but won't be playing in the tournament next season with Sporting as the club finished third in the Primeira Liga.
Martins is understood to have a €60m release clause in his current deal but the unrest surrounding his future will likely make the Cape Verde-born forward available at a cut-price this summer.