The 25-year-old midfielder is out of contract in the summer.
Liverpool have struggled with regular injuries so far this season, with Arthur Melo the latest to be sidelined with a long-term injury.
Bayern Munich are closely monitoring the situation around Gavi at Barcelona with a view to potentially signing the 18-year-old midfielder on a free transfer next summer.
The teenager was a key player for Barca during the 2021-22 campaign, contributing two goals and six assists in 46 appearances across all competitions.
The Gunners were heavily linked with a move to the former Leeds United attacker Raphinha alongside Chelsea and Tottenham Hotspur.
There was optimism about the Brazilian remaining in the Premier League. However, he had his heart set on a move to Barcelona, who have now confirmed the winger’s arrival at Camp Nou.