Andy Murray was stunned by Mischa Zverev in the Australian Open
Leon Smith, the GB captain, admits he could still play but has urged him to rest ahead of his gruelling schedule over the next few months.
"We will continue to speak with Andy in the coming days regarding his potential involvement and if he decides he would like to be part of the team then we can of course change the nominations as necessary," said Smith.
Great Britain face Canada in Ottawa in the World Group first round tie starting on February 3.
Murray, who was knocked out of the Australian Open by Mischa Zverev at the weekend, only had two weeks off after his extraordinary run of form at the end of the 2016 season, culminating in victory at the ATP World Tour Finals in London.
His next tournament is scheduled to be the Dubai Duty Free Championships at the end of February.
Smith said: "To be honest, the best thing for his body is probably not to play, in my opinion.
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"Don't get me wrong – I'd love him to play. But, for his own good, it's better for him to rest up and train and get ready for this next period, because there won't be much time the rest of the year and this might be a really good time to do it.
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"Once you play Dubai, Indian Wells, Miami, then you hit the clay season and the grass season, there isn't much time. So this is probably the best time."
Assuming Murray sticks to his plan, it will be Dan Evans, Kyle Edmund, Jamie Murray and Dominic Inglot who take on Canada at the TD Place Arena.
Evans is set to be number one after his brilliant run to the fourth round in Melbourne, while in Edmund Britain have another top-50 player.
The Canada team has not been named yet but is set to include world number three Milos Raonic, who is through to the quarter-finals in Australia.
Raonic's presence will make Canada favourites, although their next highest-ranked player is Peter Polansky at 132.
Britain can take heart, meanwhile, from their last match without Murray in Serbia last summer, when Edmund stepped up to earn an impressive victory for the 2015 champions.
Smith said: "British tennis continues to go from strength to strength and the momentum continues to build amongst our elite players continuing to make inroads up the rankings.
"After Melbourne, for only the second week in the last 39 years, we will have three British men in the ATP world's top 50 singles rankings, as well as Jamie who ended 2016 as part of the number one doubles team.
"We know the challenge the Canadian team poses – they have vast experience in singles and doubles. But we also have a strong team with a proven track record in Davis Cup. This should make for a really competitive tie."
Britain and Canada have met only once before in the competition, with Britain coming out on top 50 years ago in Bournemouth.
The winners of the tie will play either France or Japan in the quarter-finals in April, with the losers facing a relegation play-off the week after the US Open in September.