Coventry’s other Category A+ games this season have included matches against Birmingham City, West Bromwich Albion and Leicester City.
In response, Wrexham’s owners – Hollywood stars Reynolds and Rob Mac – announced that the club would be providing free travel for Sunday’s game.
The game at the CBS Arena will be Wrexham’s final away game of the regulation season, with Middlesbrough their opponents at home of the final day.
Parkinson’s side won 1-0 at Oxford United on Tuesday evening to see them move into the final play-off spot, above seventh-placed Hull City on goal difference.
Hull are away to Charlton Athletic on Saturday but Parkinson insists Wrexham cannot be distracted by other results.
“Obviously we’ll be watching the results come in – we’ll be travelling down at that time,” Parkinson added.
“But we’re not looking or expecting any favours elsewhere.
“We’re just concentrating. We know what we’ve got to do and we’re going all out to achieve it and we’ll see if that’s good enough.
“Two games left for us and good to be in the mix – it’s obviously what we wanted.”
