The ex-Royals hardman, known as 'Parky,' masterminded League Two Bantams' extraordinary cup campaign which saw them knock out Premier League sides Wigan Athletic, Arsenal and Aston Villa to book a place at Wembley.
Bradford beat Villa 4-3 on aggregate over the two-legged semi-final to become the first ever club from the fourth tier to reach a major Wembley final this week.
They will now play Swansea City, who defeated Chelsea 2-0 on aggregate in the other semi-final, at Wembley on February 24.
And McDermott expects Reading fans lucky enough to secure a ticket to be there on the day.
"What Parky has done there is fantastic," declared McDermott. "I'm just so pleased for him and I'm sure every Reading fan feels the same because he is still a legend in these parts.
"I would imagine there will be a load of Reading fans there on the day of the final and I may well go myself."
Parkinson, 45, joined Reading from Bury for £37,500 and went on to make 425 appearances, scoring 24 goals between 1992 and 2003.
Meanwhile, McDermott is eager to avoid a cup upset himself this Saturday when Reading host League One high-flyers Sheffield United in the FA Cup fourth round (3pm ko).
Royals found themselves 1-0 down after 17 seconds at League One Crawley Town in the previous round before recovering to win 3-1.
And they were knocked out by another League One club, Stevenage, at the same stage of last year's competition.
However, McDermott's record in the FA Cup is otherwise excellent having taken Royals to two quarter finals in 2010 and 2011.
"The FA Cup is not a distraction, it's a great competition," stated McDermott. "We're in the fourth round and we're determined to go as far as we can.
"We went out to Stevenage last year but in the two years before that we reached two quarter finals which was a great achievement."
And he warned: "I know Sheffield are in a different division to us but it wasn't long ago that we were both fighting for the championship and then playing together in the Premier League.
"They are a massive club with a big support and I expect they'll bring a lot down to our place this weekend.
"They also have an excellent manager and they're going well in their division. I know it will be a hard game for us."
With McDermott set to tinker with his team, the likes of Noel Hunt, Sean Morrison and Jem Karacan are all likely to be involved, though recent £300,000 Crawley signing Hope Akpan is cup tied.
"I knew what my team would be straight after the Newcastle game last weekend," he admitted. "I'm mindful there are players around the first-team who need a game."
** READING FC defender Alex Pearce has been called up by the Republic of Ireland ahead of their friendly against Poland next month.
Pearce, 24, scored on his debut for the Republic in a 4-1 victory over Oman and is set to win his second full international cap **