Press Association Sport understands midfielder Matic and striker Costa are probable absentees from the Premier League champions’ tour to Asia, which begins next week.
Matic has been linked with Manchester United and Juventus, with Chelsea apparently closing in on his replacement.
French midfielder Tiemoue Bakayoko posted a photograph from the Premier League champions’ training ground on Friday, featuring the caption “soon” and has been linked with a £40million move from Monaco.
Costa has long been linked with a move away from Stamford Bridge, despite playing an integral role in the title triumph last term, and was granted permission to miss the start of pre-season training this week.
It has also been reported that defender Kurt Zouma could miss the tour, with a season-long loan move to Stoke City possible.