According to the UK Mirror, Enrique is set to lose his job at the end of this season, after they were hammered 4-0 by Paris Saint-Germain
Enrique was restrained from clashing with a reporter after the game, but admitted that they were “inferior” to their hosts.
“It was a disastrous game,” he said.
“It’s not difficult to explain. PSG were better than us from the start. They overcame our pressure and they were better with and without the ball. We were clearly inferior.
“I’m responsible for this so don’t look for anyone else to blame. The responsibility falls solely on me. These players have given us a lot of joy.”
Barcelona have a history of hiring former Dutch players, who have a connection with Johan Cruyff, having appointed Frank Rijkaard and Louis van Gaal in the past.
Koeman is already favourite with some bookmakers while Sevilla boss Jorge Sampaoli, Athletic Bilbao’s Ernesto Valverde and Real Sociedad’s Eusebio Sacristan are also in contention.