The 27-year-old has played in all 11 of his side's league matches in 2015-16 and Xavi, now playing for Al Sadd in Qatar, expects him to fill the void he and Carles Puyol have left.
"I'm a huge fan of Busquets and he's a very close friend," Xavi told Marca.
"He's in game-changing, match-winning form, setting up goals, getting his hands dirty and putting the opposition under pressure in their own half.
"He has to step up and lead this Barcelona team over the next few years, both out on the pitch and in the dressing room."
Barcelona are three points clear at the top of La Liga going into next Saturday's Clasico against Real Madrid and Xavi has been impressed by his former side's performances in the absence of the injured Lionel Messi.
"Based on their most recent league performances, Barcelona look the stronger of the two teams going into the game, but you never know what might happen during a Clasico," he said.
"Barcelona are on an outstanding run of form even with Messi out injured. The team are doing a really, really good job and there is plenty of competition for places. They look great to me.
"I hope Messi will be fit for the Clasico for entertainment's sake and that of the game itself. Football cannot afford to not have Messi out on the pitch."