However, Erik ten Hag's side are now said to have held positive talks over a deal for the Argentina international, who is still deciding whether to head for the Emirates or Old Trafford.
Man United are said to have tabled an offer of £39.6m for Martinez, and Arsenal have a meeting scheduled with Ajax chiefs to discuss a deal in greater detail next week, with the Eredivisie champions holding out for a £43m fee.
The report adds that Arsenal have already made contact to enquire about Grimaldo's availability, and the Spaniard would prove far more affordable than the £43m-rated Martinez.
Grimaldo only has one year left on his contract with Benfica, who are reportedly willing to accept a €7m (£6m) fee for the 26-year-old to avoid losing him on a free next summer.
Barcelona were strongly linked with a move for Grimaldo as Xavi seeks competition for Jordi Alba at left-back, but the Catalan club are now said to be closing in on the signing of Marcos Alonso from Chelsea.
Grimaldo plied his trade at Barcelona's academy before leaving for Benfica in January 2016, and the left-back has gone on to register 19 goals and 50 assists in 247 games for the Portuguese giants.
The former Spain Under-21 international - who is yet to be capped at senior level - enjoyed another productive 2021-22 season with Benfica, banking six goals and nine assists from 48 appearances in all tournaments.
Grimaldo has collected eight pieces of silverware during his time at the Estadio da Luz, winning three Primeira Liga titles in addition to one Portuguese Cup, one Portuguese League Cup and three Portuguese Super Cups.
Tavares registered one goal and two assists from 28 games in all competitions was substituted early on more than one occasion, and Arsenal are said to be open to selling the 22-year-old if they can add a new left-back to their ranks.
Marseille, Real Sociedad and Atalanta BC have all been credited with an interest in Tavares, who would supposedly command a €40m (£34.5m) figure to leave Arsenal on a permanent basis.