As reported by The Daily Star, the two aforementioned Premier League giants - as well as Serie A outfit Roma - are pencilled in for discussions over the talented frontman who, according to his agent, could be allowed to leave Portugal for a fee of between £25-30 million.
"I am waiting for Jackson Martinez's manager, Henrique Pompeo, to arrive in Italy tonight for a series of transfer meetings we'll have together," Tirri told Corriere Giallorosso in quotes featured by The Star.
"It's true, he will fly in tonight because we have some encounters to evaluate and find the right proposal for Jackson Martinez. We've got meetings set up with numerous European clubs, as he is of interest to Manchester United, Atletico Madrid, Arsenal and Valencia, but also important Italian sides.
"We believe Porto will happily do with a sum between £25m and £30m."
A formidable marksman who can lay claim to a truly excellent goalscoring record at domestic level, Martinez - who has notched 40 goals in just 60 games in a two-year spell in the Primeira Liga - could be the ideal man to succeed in the Premier League.
With Arsenal particularly believed to be on the lookout for a new striker to provide some much-needed competition to the lonely figure of Olivier Giroud, Martinez would surely be more than able to provide the competition necessary to ensure that the Frenchman does not become overly complacent.
It is true that Martinez does not have any experience of European domestic competition outside of Portugal, of course, but it is obvious that he possesses a real nous in the penalty box that can surely be transferred to a higher standard of competition without too many complications.
While Arsenal's interest in the 27-year-old is perfectly understandable, Manchester United's own pursuit of Martinez seems a little more curious.
After a dreadful 2013/14 season in which the club hit low after miserable new low under the hapless management of David Moyes, there can certainly be no doubt whatsoever that new boss Louis van Gaal needs to work in cohesion with executive vice-chairman Ed Woodward to significantly strengthen the playing squad at Old Trafford this summer.
However, whether Van Gaal - who will take charge of the Netherlands at the World Cup before officially taking the reins at Manchester United on a full-time basis - should be prioritising the addition of a new forward is a matter for intriguing debate.
Although Javier Hernandez has been reduced to a peripheral role at the club in recent times, Van Gaal is known to be a huge admirer of Dutch captain Robin van Persie and it seems odd that he might look to jeopardise that close working relationship with the signing of a striker who could feasibly take the former Arsenal man's role in the first-team.
It is worth remembering that Van Gaal is a notoriously driven and occasionally stubborn manager, however, so it could be that he is willing to risk incurring the wrath of Van Persie for the good of Manchester United's fortunes as a whole.
And although Porto seem happy to do business at Martinez's current valuation, it could be that a stellar performance from the player - who could well lead the line for his native Colombia in the absence of compatriot Radamel Falcao - in Brazil this month could see such a price increase.