The incident happened during the Premier League club's warm-weather training camp.
A source from the Catalan police in the city, the Mossos d'Esquadra, said on Friday: "There were four people who wanted to go out in the city centre.
"Everything was closed so they got a taxi to a McDonald's by the Barcelona port. At some moment the driver left the car for some reason and the four people took control of the car.
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"They eventually returned it to their hotel and we got a call from the receptionist saying they had parked outside the hotel. This happened at 5.30am. The taxi was returned to its owner at 8am," the police source said.
"The four people were not arrested but they are under investigation. They were called into the police station about a crime of vehicle theft and made statements. Their statements have been sent to a investigative judge."
A statement was later issued by the club, on behalf of the players.
"We would like to take this opportunity to apologise to our team mates, the head coach, the club and especially the supporters for the events which have been the subject of widespread and negative publicity," it read.
"We felt it important we identify ourselves as the players involved in an incident which occurred during the training camp in Spain this week out of respect for team mates who otherwise could be implicated by association."
"NOT IDEAL"
Under Spanish law, the examining magistrate investigates accusations brought in a criminal complaint before moving into a trial phase. The case is unlikely to go to trial, with such cases usually being settled with a fine.
West Brom were preparing for Saturday's FA Cup fifth-round clash against Southampton, following their 3-0 league defeat by champions Chelsea on Monday.
"The club has instigated its own investigation into the incident and the players will be subject to the full rigours of our internal disciplinary procedures," the club said.
Manager Alan Pardew told a news conference on Friday that the incident was "not ideal".
"They broke a curfew and that's unacceptable and I feel let down by that. But we still got our training in. Our focus now is on the game."
Pardew's relegation-threatened side are at the bottom of the league table with three wins, 11 draws and 13 losses in their 27 matches.
Earlier this week, West Brom sacked chairman John Williams and chief executive Martin Goodman after the club's poor results this season.
(Additional reporting by Martyn Herman; Reporting by Richard Martin in Barcelona and Hardik Vyas in Bengaluru; editing by Clare Lovell and Toby Davis)
