Captain Jacques Rudolph says Dale Steyn could help give Glamorgan "new energy" if he signs for the T20 campaign.
South African bowler is attempting to complete a visa application for a potential spell with the Welsh county.
Speaking after Glamorgan's 125 run defeat by Gloucestershire, Rudolph confirmed Steyn's move was "closer" to fruition.
"I know that he went to the Embassy to get a visa I haven't spoken to him so I can't comment further," he said.
"It's closer than initially, I would say.
"I think he will be a great addition to our team I think it's an important time for us considering the first five or six games haven't gone according to plan.
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"Perhaps a change of format and one or two new faces might just give a new energy to our environment and maybe we can kick on from there."
The defeat at Bristol was Glamorgan's third of the County Championship season that sees them winless and bottom of Division Two after five matches.
They face a four-day match against Essex from Sunday before starting their T20 challenge against Surrey at the Oval on Thursday, 26 May.
Glamorgan have already signed Australian paceman Shaun Tait for the second half of the T20 tournament, and are attempting to get Steyn in for the early part of the competition.
Steyn has made 236 appearances for South Africa across all formats of cricket, including the 2016 T20 World Cup, but is not involved in their one-day series against West Indies and Australia in June.
He has has taken 406 Test wickets, one of only 13 bowlers to break the 400 mark.