According to SportBild (h/t Sport Witness), Coutinho's proposed transfer to Barcelona didn't go through this summer because the German champions were unwilling to do business over Muller. The Brazilian would have been allowed to leave Merseyside had a deal for the Germany international been struck.
Liverpool would have been happy to invest around €100 million (£88 million) in Muller had they lost their No. 10, SportBild noted.
Barcelona's interest in Coutinho was one of the transfer stories of the summer. Phil McNulty of BBC Sport highlighted that despite the player handing in a transfer request, three bids were rejected for his services, with the final offer amounting to around £114 million.
Barcelona president Josep Maria Bartomeu told TV3 (h/t Football Espana) the Reds were demanding €200 million (£176 million) for Coutinho.
Muller would not have been a direct stylistic replacement for Coutinho had he moved to Anfield, though he's a player who would be fascinating to watch in English football.
Having spent his entire senior career with Bayern, Muller has enjoyed incredible success, winning six Bundesliga titles and the UEFA Champions League. He's also shone on the biggest stage for Germany, helping the team win the 2014 FIFA World Cup.
DW Sports summed up the incredible career Muller has had on his 28th birthday recently:
Liverpool play at a breakneck pace in the final third and that's not really Muller's game. The German is all about finding space, linking play and finishing chances when they come to him.
Indeed, Sport Witness suggested the reports from SportBild may be with a view to making Bayern look stronger after a quiet summer window:
Muller's future has been discussed recently, though, especially given the way in which he struggled for form under manager Carlo Ancelotti last term. The man himself recently said in an interview with Kicker (h/t Anthony Jepson of the Manchester Evening News) he has considered a career away from the Allianz Arena.
Even so, Muller is a player who shares a great affinity with the club's supporters, and when he's on the pitch he remains one of the most intelligent forwards in the game. Therefore it is no surprise that Bayern weren't willing to do business.