Pellegrini is well-regarded by advisers of Blues owner Roman Abramovich.
The Chilean has guided Malaga into the last 16 of the Champions League this term, despite financial turmoil at the club.
And Pellegrini has also led the Andalusian side into fourth in the La Liga table.
According to Spanish TV station Punto Pelota, Chelsea have made contact with the 59-year-old in recent days.
The vastly-experienced coach would no doubt be tempted by a switch to the Premier League
More of Malaga's stars are set to be sold at the end of the season and the club is facing a ban from European competition due to their money woes.