The 22-year-old moved to Camp Nou from Borussia Dortmund for £136 million ($170m) back in 2017, replacing Neymar in Ernesto Valverde's set-up after the Brazilian had joined Paris Saint-Germain earlier that summer.
Dembele showed signs of improvement last term, contributing 13 goals and eight assists in 41 matches across all competitions, however, there has been some suggestion he could be sold during the current transfer window.
Bayern are one of a number of top European clubs thought to be chasing the ex-Dortmund star's signature, but no formal offers have yet been submitted.
Thiago, who has played against Dembele in past Klassiker fixtures, admits he "would like" to play alongside the pacey winger in Germany, as Bavarian boss Niko Kovac looks to bring in a couple of extra reinforcements ahead of the 2019-20 campaign.
"Dembele is a great player," Thiago told Bild . "But I am not the sporting director who decides if a player will be bought or not.
"As a football player and one who played against him I can say: 'He is a very good footballer'.
"I would like to play with all the great players who would love to come to Bayern."
The German champions have already signed Jann Fiete-Arp, Benjamin Pavard and Lucas Hernandez during the summer window, but the Allianz Arena has also seen a number of high-profile departures.
Veteran duo Franck Ribery and Arjen Robben left the club at the end of last season, Mats Hummels rejoined Dortmund in June and James Rodriguez has returned to Real Madrid after a two-year loan spell.
Thiago acknowledges more changes will be necessary for Bayern to compete at the same level next term, as he added: "It's a radical change, many important players left the club.
"It can always be a complicated year if important players leave. That's football. From my point of view, we have a great team.
"But, regarding the players who left, we will have to make reinforcements to achieve our goals next season."
The Spain international also praised £68 million ($85m) signing Hernandez , tipping the former Atletico Madrid ace to have a big impact in the Bundesliga.
"He is a great player who really wanted to come to Bayern," said Thiago. "I saw him at Atletico Madrid and the French national team. Physically, he is a machine, very strong! A very passionate player. He comes as a world champion with big experience. He is here to have some fantastic years."