Spanish outlet Don Balon claim that the German champions are keen to add Rakitic to their ranks ahead of the coming season and are prepared to offer the midfielder €9m across the next four seasons, having already had a similar offer rejected by the player's Croatian international teammate Luka Modric.
Don Balon suggest that Barcelona may well be tempted by the sizeable offer from Bayern, especially given the large number of midfielders currently playing for the Catalan side.
The club already has the likes of Philippe Coutinho, Sergio Busquets and Andre Gomes who are capable of playing in midfield, though the recent loan of Paulinho to Chinese club Guangzhou Evergrande might make Barca think twice about parting with yet another midfielder.
Rakitic and Modric have been the stars of Croatia's impressive World Cup run, creating endless chances in midfield with their range of passing and link-up play.
Though both players had already earned acclaim and respect prior to the tournament through playing for two of the world's biggest clubs, both midfielders have become increasingly popular and in-demand as a result of their performances in Russia.
Perhaps the greatest example of the two midfielders' contribution to the Croatia side was their 3-0 win over Argentina in the group stages, which saw both Rakitic and Modric score a goal and completely run the midfield for the entirety of the match.
Croatia will face England on the 11th of July in the semi-final of the World Cup, with the winner facing one of Belgium or France in the final.