The 28-year-old, who moved to Camp Nou on a free transfer last year after running down his contract at Lyon, scored 13 times and contributed two assists in 38 appearances for his Catalan club last term.
Memphis's current deal is due to expire next June, though, and there has been a host of speculation surrounding his future in recent weeks, with Barcelona planning to further improve their attack this summer.
Arsenal have been credited with an interest in the Dutchman, while a number of other clubs are believed to be keeping a close eye on the developments.
According to Italian journalist Fabrizio Romano, Memphis's advisors met with Barcelona on Monday to discuss the possibility of a new contract at Camp Nou.
Romano claims that the attacker is happy at Barcelona and wants to sign a new deal, but the Catalan giants are keeping 'all options open' and will listen to any offers that arrive.
"I came here wanting to play for the team. I want to be important for the team next year and for several more years," Memphis told reporters when questioned on his future towards the end of last season.
The forward scored 12 times and registered two assists in 28 La Liga appearances last term, but he found it difficult to make his mark in Europe, failing to score in six Champions League outings before netting only once in three fixtures in the Europa League.
Memphis had been a key player for Barcelona in the first half of the campaign, but he struggled with a hamstring problem towards the end of 2021 before picking up an Achilles issue, while the January additions of Ferran Torres, Pierre-Emerick Aubameyang and Adama Traore restricted his game time.
The Dutchman did feature in Barcelona's final six league matches of the campaign, though, finding the back of the net against Mallorca and Celta Vigo.
A recent report claimed that the Catalan side want Memphis to do a full pre-season before making a decision on his future, and Ansu Fati's fitness, in addition to their moves in the transfer market, will have roles to play.
Barcelona have the option to sign Traore on a permanent basis from Wolverhampton Wanderers this summer, but it appears likely that he will be heading back to his parent club.