Current world No 1 Matthew, from Sheffield, goes into the event he won for a third time last year as favourite, with second seed Willstrop expected to face him in Sunday’s final.
Willstrop, 27, from Leeds, won the event in 2007 and 2008, bookended either side by Matthew’s other two successes.
If the two do meet in the final, it would require Willstrop to produce a first win over his Yorkshire rival since December 2007 when he defeated Matthew in the English Open in Sheffield.
Both men get their campaigns underway today, with Matthew taking on Chelmsford’s Neil Hitchens, while Willstrop will face Charles Sharpes, who defeated Scotland’s Kevin Moran to make the main draw.
Should Matthew prevail, he will equal the record of four titles won by Phil Kenyon during the 70s and 80s.
“A fourth title would be amazing,” said Matthew. ““I love playing in Manchester and have always had a good record there.”
In the women’s event, Harrogate’s world No 2 Jenny Duncalf will look to win her third title, adding to the success she enjoyed in 2007 and 2009.
She begins her campaign against Birmingham’s Sarah-Jane Perry, currently ranked 173 places