ESPN reported in February that both Manchester United and Real Madrid want to sign Martinez, although the Premier League side acknowledged at the time their pursuit is likely to end in disappointment due to the competition in the striker.
Sources at Barca, who have been in talks with Inter regarding a deal for months, believe a number of the continent's wealthiest sides, from England, Germany and France, have also been tracking Martinez.
In addition to United and Madrid, Paris Saint-Germain could also be in the market for a striker with Edinson Cavani set to leave on a free this summer and the French champions unlikely to take up an option to sign Mauro Icardi on a permanent basis from Inter -- which in turn could force Inter to sell Martinez as they, like a number of clubs, attempt to minimise the economic effects of the coronavirus crisis.
Barca are worried their hand could be weakened due to the interest in Martinez around Europe. They don't want to become embroiled in a bidding war, with other clubs likely to be able to offer Inter a better package and the player a bigger salary.
Martinez, 22, has a release clause of €111 million which is active for the first two weeks of July. However, Barca have always been loathe to pay that much and have proposed various swap deals to the Italian club.
The uncertainty around the transfer market provoked by the coronavirus pandemic has enhanced Barcelona's need for Inter to lower their demands and consider accepting players as makeweights.
Barca's vice president Jordi Cardoner told ESPN that exchanges "will be part of the game" moving forward and said now is the time for the club to "be creative" as they look to rebuild their squad during a period of financial precariousness.
In preliminary negotiations with Inter, sources explained to ESPN that the Serie A side have shown an interest in midfielder Arturo Vidal, who previously worked with Inter coach Antonio Conte at Juventus, and right-back Nelson Semedo.
Sources have told ESPN that Martinez prefers a move to Catalonia, where he would link up with international teammate Lionel Messi. In that sense, Barcelona remain optimistic of landing him.
One source compared the situation to the drawn-out signing of midfielder Frenkie de Jong and explained that the club are hopeful this saga will end with a similar outcome. PSG and Manchester City both made big offers to the Netherlands midfielder before he was eventually convinced to join Barca.
The Spanish champions see Martinez as a player who can rejuvenate their attack, provide support for Messi and then, in the long-term, replace Luis Suarez as the club's No.9. The Uruguayan turned 33 in January and has long spoken about the club's need to sign a replacement for him.
Martinez joined Inter from Racing Club in 2018. Before the coronavirus ground football around Europe to a halt, he had scored 16 goals in 31 appearances this season, including one against Barca at Camp Nou in the Champions League.