Deulofeu, 23, returned to the Nou Camp during last summer's transfer window but has been limited to just nine starting appearances in La Liga this term and has not featured for Ernesto Valverde's side since late November.
His opportunities could be further limited in the second-half of the 2017-18 season with Ousmane Dembele fit once again after injury sidelined him for four months just three games into his Barcelona career back in September.
The seemingly inevitable arrival of Philippe Coutinho during the mid-season window could force Deulofeu closer to the Barcelona exit, with Inter interested in taking advantage of the situation.
Inter club director Piero Ausilio told Mediaset Premium on Friday: "There have been no formal offers for Deulofeu, but we are paying attention to the situation," Football Italia report. "If there are the conditions to try something, we know the characteristics we are looking for. Deulofeu could be the right profile, but he isn't the only one."
Deulofeu, who previously had a stint in Italy on at AC Milan last season, could present a more affordable option for Inter who are not prepared to break the bank during the mid-season window.
Manchester United's Mkhitaryan has been touted as another possible option for the Nerazzurri, having fallen out of favour at Old Trafford. The Armenia international has been replaced at half-time in his last two starting appearances, fuelling speculation that the club may choose to offload him during the January window.
But with Inter keen to keep in line with Financial Fair Play regulations, manager Luciano Spalletti admits the club simply cannot afford to pay what United would demand for Mkhitaryan.
"To keep saying we need to have a big transfer campaign, after the club has made it clear there are certain parameters to be respected, seems to me the best way to get hurt," Spalletti said.
"You can say names — Mkhitaryan, [Paris Saint-Germain midfielder Javier] Pastore, [Bologna forward Simone] Verdi. But they'd cost €30 million and we don't have that."