Murray completed a 6-3 6-0 6-3 victory over 16-year-old Borna Coric on Friday before Ivan Dodig brushed aside Dan Evans in Great Britain's to level the tie.
Murray was expected to partner Colin Fleming in Saturday's doubles, but Jonny Marray could be drafted in if Murray does not feel up to it.
"The doubles isn't until the afternoon so it give us plenty of time to assess it," British captain Leon Smith said of Murray's back injury.
The Wimbledon champion admitted he was not feeling 100 per cent fit.
"My back is a little bit sore," he said.
"The change of surface is difficult, but after a couple more matches I'll have some time to rest, so let's just get the win this weekend."
Murray also added that he expected Coric to be a decent player in the future.
"The first five or six games were tough.
"He was solid, he fought for every point. When he gets physically stronger, he's going to be a very tough player. The future is obviously very bright for him."
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