Pardew is struggling to persuade West Brom's Chinese owner to retain his services.
Jonny Evans, Gareth Barry, Jake Livermore and Boaz Myhill admitted they had broken a team curfew when they took a taxi from Barcelona city centre at 5.30 am (0430GMT) on Thursday morning.
Mossos d'Esquadra - Catalonia's regional police force - previously told BBC Sport the four wanted to go out in Barcelona, but found everything closed so took a taxi to a 24-hour fast-food restaurant. Sources in Spain suggested this was down to the taxi driver deciding against pressing charges.
The local judge had been asked to consider whether there was enough evidence to bring charges of "theft and vehicle theft".
Thai court hands surrogate kids to Japanese father
They were subsequently cared for by the Thai state, while another four infants were deemed also to have been fathered by the same man.
Last in the Premier League, West Brom were in Barcelona for a mid-winter training trip. That inquiry is expected to last two weeks and will see the quartet interviewed individually by club directors.
Warm weather training camps are nothing new, managers often see the benefit of providing a new environment for their players to refocus their minds ahead of a crucial block of the season.
Pardew's position is under scrutiny after the events of last week, which started with defeat at Chelsea and included the shock dismissals of chairman John Williams and chief executive Martin Goodman by owner Guochuan Lai.
On it, the Baggies were knocked out of the FA Cup at the weekend by Southampton.