The Catalan giants were beaten by three clear goals in Portugal, and the result means that the club have lost their opening two Champions League group-stage games to sit bottom of Group E.
According to Romano, there are 'crucial hours and days ahead' when it comes to the Dutchman, and Barcelona have already identified legendary midfielder Xavi as a possible replacement.
Belgium boss Roberto Martinez is also allegedly being considered by Barcelona, who have a huge La Liga match against Atletico Madrid at Wanda Metropolitano on Saturday.
Blaugrana, who lost Lionel Messi on a free transfer over the summer due to their financial problems, are currently sixth in La Liga, boasting 12 points from their opening six games during an unbeaten start.
Koeman has now won 37, drawn 12 and lost 13 of his 62 games in charge of Barcelona, and the 58-year-old's contract at Camp Nou is due to expire at the end of the 2021-22 campaign.
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