Morkel has spent an extended winter in Sydney, where his wife is from. His ability to train outside has been limited, so Surrey will assess his readiness to return to action in the coming days.
Having lost to Essex on Tuesday, Surrey’s next game is on Saturday, against Hampshire, at Arundel.
Surrey were forced to dip into the loan market last week as they had six England players unavailable and a series of injuries among their fast bowlers. Of those, Jade Dernbach appears the closest to a return.
Coach Vikram Solanki said: “We need to assess the players who have played in this game [against Essex] and be smart, because we have plenty of cricket coming up.”