The Catalan giants have been strongly linked with the Argentina international over the last few months but have thus far been unable to agree a fee with Inter.
Martinez's agent recently said that his client would not be on the move this summer, with Barca having limited finds due to the financial impact of the coronavirus outbreak.
According to Marca, the La Liga giants are preparing to make one final approach for the 23-year-old, although it remains to be seen whether Inter are prepared to drop their £90m asking price.
Suarez's departure has left Barca short of options in the final third of the field, and Antoine Griezmann could lead the attack for their first league match of the season against Villarreal on Sunday.
Martinez enjoyed an impressive 2019-20 campaign at San Siro, finding the back of the net on 21 occasions in 49 appearances in all competitions, including five goals in six Champions League outings.