Grayson pitted his wits against Wenger in three FA Cup games when he managed Leeds United.
In January 2011, Leeds drew 1-1 at the Emirates Stadium in the third round, before the Gunners won the replay 3-1.
The following year, again in the third round, Arsenal beat Leeds 1-0 at the Emirates.
Grayson will be hoping it is fourth time lucky when North End face the Premier League giants in the new year.
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“For myself, I can pit my wits against Arsene Wenger,” said Grayson in an interview on PNE’s official website.
“I have done it before a couple of times when I was at Leeds and the players will be looking forward to it.
“They will be desperate to play and hopefully it will add a bit more spice to the team over the next few weeks.
“Everyone will look to improve to get some results and stake a claim for a place when the tie comes around.”
Like every manager whose club lands a big FA Cup tie, Grayson will be anxious that the focus remains on their league form until January.
Preston have six games in the Championship before facing the Gunners, starting with Saturday’s derby clash against Blackburn.
They have away games at Nottingham Forest and Bristol City, before hosting Leeds on Boxing Day and Sheffield Wednesday on New Year’s Eve.
On January 2, North End visit Burton, then the Gunners come to town.
“We are all looking forward to it but the cliché is that we have too many games before then to worry about Arsenal,” said Grayson.
“It’s going to be brilliant in the next few weeks.
“With the next four home games being Blackburn, Leeds, Wednesday and Arsenal, when you get the numbers in here it makes it a place that everyone wants to be part of.
“Arsenal have a fantastic history and will be looking to get some silverware this year.
“On the other side of that, we will be looking to progress to the fourth round.
“We have quite a few league games to concentrate on but when it comes around, it will be great for everyone.”
Arsenal were visitors to Deepdale in the FA Cup in January 1999, the Gunners winning 4-2 after Preston had led 2-0.
The sides met later the same year in the League Cup at Highbury, Arsenal running out 2-1 winners.
In the FA Cup, North End have met Liverpool, Chelsea and Manchester United at Deepdale in the last eight years and have yet to cause a shock. Could things change this time?