Xavi's side are said to be on the lookout for a new left-sided defender to provide competition for Jordi Alba, who turned 33 earlier this year.
Alba still has another two years left to run on his contract at Camp Nou, but Barcelona are expected to soon start planning for life without the veteran Spaniard.
Celta Vigo's Galan is understood to have been identified as an ideal acquisition, but the 27-year-old will not arrive in Catalonia on the cheap.
Galan only arrived at Celta Vigo from Huesca in the summer of 2021, and he still has four years left to run on his contract with Eduardo Coudet's side.
According to Mundo Deportivo - via the Daily Mail - Galan possesses an €18m (£15.2m) release clause in his Celta contract, and Barcelona must trigger it if they are to prise him away from the Estadio de Balaidos.
Barcelona could try to negotiate a lower fee for a player whom Xavi is said to admire, but Celta are not prepared to make life easy for La Blaugrana in negotiations.
Coudet is understandably keen to keep hold of Galan, but Celta will reportedly accept the left-back's exit if Barcelona agree to pay the entirety of his release clause.
Last season, Galan registered three assists in 39 appearances for Celta Vigo in all competitions during his debut campaign, as the Sky Blues just missed out on a top-half finish in La Liga.
The former Cordoba youngster, who started all but one of his side's La Liga matches, cost Celta Vigo a mere £3.6m to prise away from Huesca last year.
Barcelona were initially thought to have made Chelsea's Marcos Alonso their priority left-back target, but a move for the 31-year-old is now in jeopardy.
Xavi's side have already beaten Chelsea to the signing of Raphinha this summer, as well as agreeing a new deal with Ousmane Dembele amid reported interest from the Blues.
The two sides have now clashed again in the transfer market, with Barcelona expected to successfully hijack Chelsea's proposed £55m deal for Sevilla defender Jules Kounde.
As a result, Chelsea have supposedly blocked Alonso and Cesar Azpilicueta from completing moves to Barcelona after weeks of speculation, although both players could now leave on a free transfer in 2023.
Andreas Christensen has already made the move to Barcelona after running down his Chelsea contract, joining Franck Kessie, Robert Lewandowski and Raphinha in La Liga for the 2022-23 campaign.