The Swiss attacker appears to be just one step away from signing for the Bundesliga leaders and a transfer could be announced in the next few days
The 20-year-old is expected to sign a four-year contract with the Bundesliga giants after the two clubs agreed a reported €9 million deal for the player.
Sky Sport News reports that a car with Swiss plates was spotted at Bayern's headquarters earlier on Tuesday afternoon.
Bayern turned to Shaqiri after Borussia Monchengladbach star Marco Reus snubbed the Bavarians in favour of a move to Borussia Dortmund at the end of the season.
German sources suggest that Bayern will announce Shaqiri's signing in the coming days.
The Switzerland international will play against Bayern later this month when Basel lock horns with the Bundesliga outfit in the last-16 of the Champions League.