"Xavi was a great player, a football icon, and now he is back home at Barcelona. I hope he has a lot of success with the group that we are," said the 29-year-old.
"Given the person he is, he will definitely do very well at Barcelona."
Despite being nothing more than a bit-part player under Koeman since returning to Barca 18 months ago from a season-long loan at Bayern Munich, Coutinho has nonetheless earned himself a recall to the Brazil squad for this month's World Cup qualifiers against Colombia and Argentina.
Coutinho suffered a knee injury last December that ended his season and following two operations he has played little this campaign.
"It's like it was my first time," said Coutinho of his surprise recall to coach Tite's squad after a year out.
"It's always an honor to wear this jersey."
Brazil can book their ticket to Qatar if they beat Colombia on Thursday, and a draw would also be enough should Uruguay lose to Argentina the next day.
Barcelona sit ninth in La Liga after winning just four of their opening 12 league matches.
