The Spanish side were previously reported as having reached a verbal agreement with the player, who is said to have already accepted personal terms with the side following a conversation with manager Diego Simeone.
Martins, who has been a Sporting CP player since 2015, was one of many of the club's stars who cancelled their contracts in the wake of the tumultuous end to the season that saw them publicly humiliated by the club president, miss out on the Champions League in their last match of the campaign and suffer an attack at the hands of masked thugs at their training ground.
Sporting, however, still maintain some control and are still due compensation. According to Diario AS, the Portuguese outfit want at least €45m for the winger, but Atleti are only willing to pay €15m, with a further €10m in potential add-ons.
The Rojiblancos feel they have the edge in negotiations, based on Sporting's current status, yet it will take FIFA 's intervention to settle things as the clubs have so far failed to resolve the transfer amicably.
Martins, meanwhile, is still on holiday after playing in the World Cup with Portugal, who were eliminated from the tournament by Uruguay in the round of 16.
He is expected to end his vacation at some point next week, with Atletico waiting to ramp up their chase when he returns.