Murray missed both of the nation's ties in 2012 and the weekend drama of their Europe/African Zone Group I play-off with Russia.
World number 325 Dan Evans and No.217 James Ward won in Coventry on Sunday to complete a first victory from two rubbers down for Britain in 83 years.
"He said he would play, so it’s something he’s very much still set for in September," said a spokesman for the Scot.
Murray was at the Ricoh Arena to support Leon Smith's team.
The draw for the September 13-15 tie will be held on Wednesday, with possible away opponents being Rafael Nadal's Spain, Austria, Croatia, Belgium or Japan. Alternatively Britain could secure a home clash with Roger Federer's Switzerland, Germany or Australia.
The match will take place only five days after the US Open final, which Murray will hope to be involved in as he seeks to defend his maiden Grand Slam title.
When Scot Smith took over from John Lloyd in 2010, Britain had suffered consecutive relegations from the World Group to Europe/Africa Zone Group I, then Group II.
His first task was a relegation play-off against Turkey to avoid going down to Group III - and Britain survived.
Smith oversaw a return to Group I and now hopes to make it two promotions in three years.
Britain are the third most successful team - with France - having won nine titles, but have only appeared in one final since 1937.