The Red Devils confirmed on Wednesday that Martinez had officially become the team's third signing of the summer transfer window, following Tyrell Malacia and Eriksen to the club.
According to the Manchester Evening News, both Eriksen and Martinez featured for the club against Wrexham, with the former on the scoresheet in the friendly fixture.
The report claims that a number of senior players were involved in the contest, with head coach Erik ten Hag keen to give minutes to those that struggled for action during the team's pre-season tour of Thailand and Australia.
Eriksen allegedly opened the scoring against Wrexham, who then levelled through Aaron Hayden, but Man United scored three more times in the second period to record a 4-1 win.
Cristiano Ronaldo is believed to have watched the match amid the speculation surrounding his future, with the Portugal international now back in Manchester.
Meanwhile, Bruno Fernandes, Marcus Rashford and Harry Maguire are also said to have watched on from the touchlines after taking part in an earlier training session.
Raphael Varane is believed to have played some part in the contest, while there have been claims that Alejandro Garnacho was one of the Man United players on the scoresheet in the second period.
Man United are currently preparing for their final two pre-season friendlies of the summer against Atletico Madrid and Rayo Vallecano, which will take place on Saturday and Sunday respectively.
The 20-time English champions will then have another full week of training before opening their 2022-23 Premier League campaign against Brighton & Hove Albion on August 8.
Man United played four times during their summer tour of North America, opening their preparations for the new season with a 4-0 victory over bitter rivals Liverpool in Thailand.
The Red Devils then travelled to Australia, where they played three times, beating Melbourne Victory and Crystal Palace in Melbourne before travelling to Perth to take on Aston Villa, with the contest finishing 2-2 after Calum Chambers came up with a late equaliser for Steven Gerrard's side.
Man United are still working on new signings for the 2022-23 campaign, with Barcelona's Frenkie de Jong and Ajax's Antony thought to be leading targets for the club.
Ten Hag is believed to be planning to use the majority of his first-team players against Atletico on Saturday before deploying a second-string side against Rayo in what will be his first game in charge of the club at Old Trafford.