Former British number one Draper has only played 15 matches in the past year because of bone bruising in his serving arm and tendinitis in his knee.
As a result he has dropped to 160th in the world rankings.
Reaching the Eastbourne semi-finals in his comeback tournament last week – having not played since April – was a promising sign.
The rigours of five-set matches will be a sterner examination of Draper’s fitness, particularly against American sixth seed Fritz in a plum first-round draw.
Draper has turned to British former world number one Andy Murray for guidance in dealing with his injury setbacks and the expectations which he might face from home fans at Wimbledon.
In May, Draper announced he has brought the two-time Wimbledon champion – his childhood idol – into his coaching team for the grass-court season.
Murray told BBC Sport earlier this month he wants the partnership to be a longer-term arrangement – and Draper feels the same.
“Having him around helps a lot. Him just being here, being in my presence, not just now, but the last few weeks, has really helped my confidence,” said Draper.
“It’s not been an easy time at all. [Murray] being around to help guide me through this period, get me back to being on court, get me back to competing, has been very, very special.
“I think it’s just the start. I think it will be a great partnership.”
