There is currently speculation surrounding the Netherlands international's future, as his contract at Camp Nou is due to expire at the end of June.
Manchester United continue to be linked with the 28-year-old, with the Red Devils looking to sign a new forward before the end of the month.
However, speaking ahead of Wednesday's Copa del Rey contest with Intercity, Xavi said that he is determined to keep hold of Memphis for at least the rest of the season.
Xavi also insisted that Memphis "will get minutes" despite being down the pecking order in terms of the positions in the final third of the field.
"I don't want anyone to leave. With these players, we will compete. I'm happy with what I have. Memphis can help us in attack. He will be important and he will get minutes," said the head coach.
Memphis has only played three times for Barcelona this season, having struggled with injury problems in the first half of the 2022-23 campaign.
The attacker returned to fitness at the 2022 World Cup, though, representing Netherlands on five occasions at the competition, finding the back of the net against the USA on December 12.
Memphis is expected to be in the side when Barcelona take on Intercity in the last-32 stage of the Copa del Rey on Wednesday night.
Xavi has said that the competition is important for the club this season despite La Liga being the priority.
"It's always very difficult for us in the first game of the cup, I remember eliminations against Figueres and Gramanet, and it's a round full of surprises. We have Intercity's report because they played against the reserve team," the Spaniard said ahead of the clash with Intercity.
"For us La Liga is the most important objective outside of the Champions League, but we are very excited about the Cup and it is very important, we want to compete for it."
Xavi also confirmed that Eric Garcia and Ronald Araujo will be among the players to receive minutes.
"The idea is to rotate and give minutes to players who haven't played for a long time, such as Eric and Araujo," he added.
"He (Araujo) is one hundred per cent. He will start tomorrow and he will help us with his leadership, with his aggressiveness."
Barcelona are the most successful side in the history of the Copa del Rey, winning the trophy on 31 occasions, with their last triumph in the competition coming in 2020-21.