The Spain international graduated out of the famed academy system in Catalunya to make over 100 senior appearances for the Camp Nou side.
Thiago only committed to a new contract through to 2021 last summer, but Ter Stegen is hoping that Barca will make moves in the next window to bring the 27-year-old back to La Liga.
The Germany international goalkeeper told Sport Bild: “I would like to have Thiago at Barca. His playing style suits us and from our viewpoint he is an interesting player.
"Thiago is a special type of player. He definitely would offer us different possibilities. If a transfer happened, it would be brilliant both for him and for us.”
Bayern have hinted that they could be open to offers for Thiago, despite maintaining that no formal approaches have been made as yet.
Karl-Heinz Rummenigge, CEO of the German giants, told Sport Bild: “No club has contacted us, nor Thiago. We still plan with him. However, I must say the midfield is stacked.
“We have three or four places for nine players. The squad is great, but if we sell players, I don’t rule out that we will do something in the market.”
Thiago made 31 appearances for Bayern across all competitions in the 2017-18 campaign, but did face criticism from a club icon in the spring which fuelled talk of a possible summer switch.
Lothar Matthaus said: “Thiago hasn't made the difference in the big games. I actually think he's good but he's been a shadow of his former self recently.
“Thiago has disappointed me in the past few weeks. I don't know where his head is.
“With these performances, he's not a player for Bayern Munich. If a suitable offer is on the table, then Bayern should think about it.”