Carrick's side lost 3-0 at home to Bournemouth over the weekend, which stretches his winless run to eight games across all competitions, and the former midfielder is under major pressure at Old Trafford.
However, following showdown talks with club officials, a call has now been made to keep him in place for at least the trip to Stamford Bridge.
Eddie Howe and Julian Nagelsmann are the two frontrunners to replace Carrick on a permanent basis, but neither would be appointed at such short notice, and the situation will be looked at after the Chelsea game.
Howe has reportedly indicated his willingness to discuss a move to replace Carrick, if the club do make the move to remove him next month, but the experienced coach would also carry a £6M compensation fee paid to former club Newcastle United.
Following the Chelsea clash, United have two home matches before the November international break, against Aston Villa and AS Roma.