BBC Sport understands that Stamford Bridge executives and players are backing the Italian as their first choice for the role.
The report also notes that the interim coach has already been asked to make preparations for next season and organise a pre-season tour of the US.
Di Matteo has been in charge at Chelsea for 15 games, during which the team has played out 10 wins, four draws and one defeat.
He has also guided the Blues to both FA Cup and Champions League finals, prompting Chelsea technical director Michael Emenalo to interview him for the managerial post.
However, the club's owner Roman Abramovich will not make an appointment until the end of the season.