Following his defeat in the US Open semi-final last week, Draper has recovered quickly.
Although the 22-year-old is eager to participate, Leon Smith, the captain, is evaluating his health.
British No. 1 is probably going to be quite popular in Manchester following his time in New York.
Jack Draper will be given until the very last moment to prove his fitness as the British No 1 looks to shake off fatigue to play in Great Britain’s Davis Cup opener on Wednesday.
Draper, who arrived in Manchester to link-up with his team-mates on Tuesday lunchtime, conceded after his career-best run to the US Open semi-finals that he was ‘banged up’ following defeat to world No 1 and eventual winner Jannik Sinner.
And while team captain Leon Smith is thrilled to have his highest-ranked player among his stable of players here, ‘risk versus reward’ is at the forefront of his thinking with ties against Argentina and Canada, on Friday and Sunday respectively, following Wednesday’s opener against Finland.
‘We are absolutely thrilled that he’s coming,’ Smith said. ‘That shows his commitment.
‘I have spoken to him a lot about Davis Cup. He obviously came to Colombia last year and then was involved in what we did in September and November.
‘You can tell straight away that he gets Davis Cup: he plays with passion, pride, fight, and you mix that with the fact he’s a top 20 player with unbelievable quality, he’s going to be a very important member of the team not just this week but for many, many, many years to come.
‘He absolutely loves it and his commitment by coming here just shows that.’
Pressed on whether Draper, who is practising off-site in Manchester on Tuesday, has a shot of playing in one of the singles openers, Smith is playing the long game, hinting that his star player will be given additional rest.
‘I have to select the team to do what is best, not just for tomorrow, but also we have really important matches at the weekend as well so we just have to weigh up risk versus reward a little bit,’ he said.
‘Until we get on the court and start doing some stuff it’s quite hard to tell how that feels [with him].