The 19-year-old, who joined the Pilgrims last month on an initial month-long deal, has made five appearances for Argyle.
The club have now seemingly reached an agreement with Chelsea director Frank Arnesen to prolong Clifford's stay which was due to come to an end on Friday.
Reid told the club's official website: "We have been delighted with Conor's contribution over the last month.
"I have been in discussions with Frank Arnesen and we are expecting the paperwork to be completed by the end of this week.
"I would again like to express my gratitude to Chelsea for allowing Conor to continue his development with us."
Source: PA
Source: PA