Chelsea dismissed manager Liam Rosenior on Wednesday after their collapse at Brighton.
The result leaves Chelsea struggling to qualify for the Champions League this season.
Rosenior lasted barely three months in charger at Stamford Bridge and has now been replaced by McFarlane.
The Mirror says Chelsea are willing to go with MacFarlane to the end of this season before making a permanent managerial appointment over the summer.
Chelsea directors were reluctant to act on Rosenior, appreciating how he mixed with staff and the board. However, the performance at Brighton and Rosenior's reaction forced their hand.
Sources say the parting has been amicable, with Rosenior and staff informed of the decision well before it was announced late on Wednesday afternoon.