Moses Mazomba, 24, came to Glasgow in 2009 and became a well-known member of his community in Springburn and a well-liked member of Cartha Queen's Park Rugby Club.
He is currently being held by immigration officials from the Home Office after his visa expired.
He originally came to the UK for medical treatment for an eye condition, but when his visa ran out he was told he had to leave.
But Mr Mazomba's lawyer, Fraser Latta, is preparing a last-minute appeal in a hope to get the UK Government to think again.
Mr Latta said: "We are in the process of compiling a substantial amount of additional evidence in his case.
"I've received a lot of supporting letters for him.
"He's due to be removed to Zimbabwe on Thursday. He is extremely concerned about any proposed removal."
Nadia Maloney, from the Unity Immigration Centre, who have helped with Mr Mazomba's case said: "Moses initially came here on a medical visa for corneal transplants but has only had one eye treated.
"During his time in Glasgow Moses has integrated into society and created a life for himself. He is a valued player for the Cartha Queen's Park Rugby Club. He has made many good friends and has had a significant positive impact in his community.
"Moses is desperately running out of time and is becoming desolate.
"He is a wonderful young man who belongs in Glasgow and has been a credit to his community."
Gary Grant, head coach at the South Side rugby club said: "Moses is a lovely young man.
"Everybody was pretty shocked when they found out he'd been detained. He is popular, he's tenacious, he worked really hard."
Club members have put their names to a 500-strong petition calling for Moses to be allowed to remain.
A Home Office spokesman said: "We only return individuals if both we and the courts are satisfied they have no legal basis to remain in the country.
"Mr Mazomba was first refused asylum in September 2008. This decision was upheld by an independent High Court judge at appeal. He has been in the country without valid leave since 2009.
"When someone is found not to have a right to be here, we expect them to leave voluntarily. If they fail to do so, we will seek to remove them."