That will be a little harder to achieve for Parker, a former WBO champion on the comeback trail after a frustrating 2019 during which he fought only once – a stoppage win over Alex Leapai in New York.
But such are the stakes as Parker attempts to work his way back into a mandatory challenger position after he lost his world title in 2018, complacency at Ford Center at The Star, a 12,000-seat indoor stadium used by the Dallas Cowboys as their main training facility, shouldn't be an issue.
"My message to him would be 'come prepared' or 'come with everything you've got'," Parker said of his own advice for Winters, a 39-year-old with a 13-2 professional record.
"A lot of the pressure is on myself and my team because no one knows much about Shawndell Winters. Even though he's had two good wins against undefeated fighters and 13 wins with 12 knockouts, people still don't know who he is ... I'm expected to win but if you take it lightly that's where trouble happens."
Fury warmed up for his second bout against Wilder – the first, in Los Angeles in 2018, was declared a draw – with an awkward unanimous decision victory over Otto Wallin in September last year.
The man who has battled addiction issues and mental health problems and who appeared to reinvent himself as a front-foot, aggressive boxer almost overnight for his TKO win over Wilder last Sunday, knows about looking beyond the next challenge.
"More than anything else, Joe is well aware that we've had two fights in the last 19 months," Parker's trainer Kevin Barry said of his charge, who has sparred 118 rounds over the past seven weeks.
"Right at the moment things could not be more significant or more important for us. I think he's in really good shape.
"The heavyweight division hasn't been this exciting for a decade. For Joe to be one of the main players in the heavyweight division is very exciting for us. We saw a tremendous performance from Tyson Fury last Saturday night, a boxing masterpiece. He just dismantled Deontay Wilder. There were a lot of gobsmacked people, including myself, who could not believe the job he did."
Parker, who wants to fight at least twice more this year, said he had backed Fury to win at the weekend.
"I always back the boxer, and he was so confident. When he first fought Wilder he was 50 per cent. Fast forward to where he is now. He's a lot better as a fighter and a person – mentally and physically."
Fury's added weight and aggression helped with increased power for a man described as having "pillows for fists" by Wilder ahead of their latest showdown, but Parker added: "Ultimately something up here [in mind] has to be switched."
He said he would like Fury to face former foe Anthony Joshua, the holder of the WBO, WBA and IBF world heavyweight titles, next.
"Wilder's indicated he wants a rematch but I feel it would be a similar result," Parker said.
"All of us in boxing and the fans want to see who is number one. I feel they should make the bigger fight happen."
Asked who he thought would be victorious, he said: "I back Fury. I feel Fury and Wilder could beat Joshua."
Joseph Parker's fight against Shawndell Winters, on the undercard of the Jesse Vargas v Mikey Garcia welterweight world title fight, will be screened live on Sky Arena on Sunday. The Parker v Winters bout is scheduled to start at 2pm.
Patrick McKendry travelled to Frisco, Dallas, with assistance from Duco Events.
