Glamorgan coach Robert Croft says the club would consider a replacement if Shaun Marsh is ruled out for some time.
Australia batsman Marsh is having a scan on his shoulder after an injury suffered while fielding in Sunday's T20 Vitality Blast defeat against Sussex.
"We'd have to consider it, that's one that (chief executive) Hugh Morris, (captain) Colin Ingram and I would have to discuss," said Croft.
Marsh has opened the batting with Usman Khawaja in the first two T20 games.
He fell awkwardly while trying to make a boundary save, called for medical attention and left the field immediately.
"Shaun's a tough guy, so it's certainly not a bruise the way he walked off holding his shoulder," Croft said.
"So we'll have to wait and see, but we hope the scan will be favourable to us."
Glamorgan, semi-finalists in 2017, have one win from two games after an emphatic 63-run win at Hampshire was followed by an eight-wicket defeat to Sussex.
"Everything we touched went to gold on Friday night, but today we weren't clinical enough with the ball and we weren't able to execute our plan," Croft told BBC Sport Wales.
"But there still moments we could have nibbled our way back into the game."
Glamorgan play Essex at Chelmsford on Friday 13 July, with the rest of their T20 campaign spread over the following five weeks.