GB waiting on Murray.
The world number four is battling to overcome the virus which forced him to pull out of the Dubai Championships this week.
He was scheduled to arrive back at his London base today and planned to see a doctor for further advice ahead of the Euro-Africa Zone Group I tie, which begins in Glasgow on Friday.
Great Britain captain John Lloyd said: "We have to see what the doctor says and then go from there.
"I can change two guys up to 24 hours before the draw so, obviously, we can leave it up to the last moment."
Murray's fellow Scot Colin Fleming and James Ward will travel with the team to Glasgow in case the British number one fails to recover.
His withdrawal would leave Britain with one of the most inexperienced line-ups they have ever fielded after Lloyd named world number 196 Josh Goodall and number 390 Chris Eaton in his team yesterday.
Both impressed in Lloyd's new play-off system for determining Davis Cup places but neither has played a tie before.
However, coach Paul Annacone insists Great Britain can beat Ukraine without Murray.
He said: "Ukraine is a great chance for these guys to get their feet wet. After watching them play at the levels they played at, I don't have any doubt that they can win, with or without Andy.
Doubles specialist Ross Hutchins is the other member of the four-strong team.
FITNESS FIGHT: Murray