Thiago enhanced his growing reputation at the European U21 Championship as he skippered Spain to another major international crown.
He netted a hat-trick in a 4-2 final victory over Italy on Tuesday, suggesting he is ready to play a prominent role at one of Europe's top clubs.
Barcelona hope he will continue to blossom at Camp Nou, but he finds himself behind the likes of Andres Iniesta and Xavi in Catalunya and made just 15 La Liga starts last season.
Manchester United, Real Madrid and Bayern Munich are believed to be among those prepared to offer Thiago the stage his talent deserves, but Pique has called on the 22-year-old forward to be patient and wait for his opportunity at Barca.
He told Onda Cero: "There is a possibility that he could leave but we have to convince him that the best place for him is Barcelona.
"Players in his position like Xavi were patient and they ended up defining an era."
Should Thiago end up leaving Camp Nou for Old Trafford, as is being widely reported, he already has one big admirer in Manchester, with United defender Rio Ferdinand among those to have been left purring at the quality Spain possess throughout their international ranks.
He tweeted after their U21 success: "Spain u21s were too much! Thiago wants the ball under pressure, he demands it anywhere. We need to produce that kind of mentality in our kids."