South Africa are hoping the Morkel brothers will be fit to return from injury in the second match of the NatWest Series on Tuesday.
The Proteas trail England 1-0 in the five-match rubber after Friday's 20-run defeat at Headingley.
Fast bowler Morne, who has been struggling with a side strain, bowled half a dozen overs in the Trent Bridge nets on Sunday in preparation for a possible comeback in Nottingham.
His elder sibling, all-rounder Albie is also making progress in his rehabilitation from a shoulder problem.
"Morne bowled the equivalent of six overs in the nets in two spells of four overs and two overs," said South Africa's assistant coach Vincent Barnes on Sunday.
"He was only operating at about 50 percent of his capacity, so we will have to step him up quite a bit on Monday if he is to make Tuesday's second match.
"Albie has also made significant progress. He took a complete part in the batting and fielding drills but at this stage is only bowling with a tennis ball under the direction of (physio) Shane Jabaar.
"Again Monday will be an important session for him."
South Africa's defeat at Headingley was their first in 10 one-day internationals and left coach Mickey Arthur to bemoan the loss of firepower with both bat and ball.
"We wanted to come out and play with our first choice side and what it does is that it also disrupts our balance hugely," said Arthur.
"At number seven and number eight we didn't have a guy who can hit the ball out of the ground.
"When you're needing a big over Albie is the guy who can hit it out of the ground for you.
"We had Johan Botha and Vernon Philander who can work it around quite nicely but they needed to be batting with someone who was in and who could hit boundaries at will so that was a pity."