The Gunners were one of several Premier League clubs linked with a potential swoop for Colombian international Martinez this summer, although Arsene Wenger eventually elected to bolster his strikeforce with the impressive £16 million capture of Danny Welbeck from rivals Manchester United.
Despite that aforementioned arrival, reports from the Daily Express claim that Wenger remains desperate to land the prolific Martinez as he seeks to further strengthen his attacking options when the transfer window re-opens for business in the new year.
Tottenham manager Mauricio Pochettino is believed to harbour a similar desire to sign the 28-year-old and it is also suggested that the club will look to offload expensive failure Roberto Soldado in order to facilitate the move.
Impressive goal tally
A mere casual glance at Martinez's quite sensational goal record is enough to provide a snapshot of the qualities he would bring to either North London outfit.
Since moving to Portuguese football from Liga MX side Chiapas in July 2012, Martinez can lay claim to an incredible tally of 69 successful strikes for Porto - nine of which have come during the early stages of the 2014/15 season.
While it is fair to say that the majority of these goals have come in a league generally deemed to be vastly inferior to Europe's top divisions, it is important to note that Martinez has also proven his talent in the Champions League and has four goals to his name already in the latest edition of tournament.
Arsenal's late decision to recruit Welbeck on transfer deadline day came as a result of Wenger finally realising that the largely inexperienced Yaya Sanogo was unlikely to able to carry the necessary load with first-choice frontman Olivier Giroud ruled out of action until January with a foot injury sustained during August's draw with Everton at Goodison Park.
The England man has enjoyed a generally positive start to life at the Emirates Stadium and a hat-trick in last week's encounter with Turkish champions Galatasaray appeared to go a long way to silencing the supporters who had previously expressed reservations over his lack of consistency and indeed ability in front of goal.
Despite this encouragement, however, Giroud's long-term absence - coupled with Sanogo's curiously persistent hamstring complaint - has ensured that Arsenal remain short of the necessary depth in the final third.
Tottenham's striker shortage
Tottenham are arguably even more in need of further competition up front, with Soldado still to prove that he is capable of adapting to the pace of the Premier League and Emmanuel Adebayor remaining frustratingly inconsistent.
21-year-old Harry Kane, meanwhile, has shown significant promise since the arrival of Mauricio Pochettino but - like Sanogo - is probably not yet ready to be relied upon to lead the line on a full-time basis.
Martinez signed an improved one-year deal at the Estadio do Dragao earlier this year and such an agreement is reported to have reduced his buyout clause from €40 million to a marginally more affordable €35 million.