Azpilicueta has been linked with the European champions virtually all year and reports in France have claimed an agreement was reached over a transfer fee late on Tuesday night.
It was also suggested the 22-year-old Spaniard, who started Marseille's opening two Ligue 1 games of the season, would sign a five-year deal at Stamford Bridge.
The fee was said to be undisclosed but it has been reported to be in the region of £7 million.
Chelsea stuck to their usual policy of not commenting on transfer speculation on Wednesday morning.
