The Swans are sitting a game clear atop the ladder, while the Tigers need to win if they are to qualify for September.
But McVeigh says the Swans will be using the match as a dress rehearsal for their upcoming finals campaign.
"It won't be hard for us," McVeigh said. "We think we play a finals brand of footy every week and our boys are ready for this game.
"We need a strong lead-up to the finals, so there will be no question that we'll be ready."
The Swans are the last side to beat Richmond, overcoming a 26-point deficit in the second quarter to record an 11-point win at the MCG back in round 14.
McVeigh said the Swans "got lucky" that day and didn't play to their usual standards.
Lance Franklin was a key reason behind the comeback victory, kicking four of the Swans' nine goals, including the only two in the fourth quarter.
In an ominous sign for the in-form Tigers, Franklin and Kurt Tippett are steadily building their partnership at the right time of the season.
Tippett, who missed the last Richmond game with a knee injury, kicked four goals in last week's victory over the Western Bulldogs, combining with Franklin for 28 touches, 13 marks and 10 of the Swans' 20 goals.
Tippett and Buddy have played the past three games together and nine together overall this year and the former feels their partnership can still improve.
"I think we're building," Tippett said.
"Nine games now and I think we've still got a lot of improvement to come.
"We haven't had a great deal of time together, not having done a full pre-season or played heaps together to date (due to injuries).
"It's something we can continue to get better at hopefully.
"We pick apart our game each week, and the relationship and our movement patterns can still improve."
Josh Kennedy (hamstring), Craig Bird (knee), Sam Reid (hip) and Ben McGlynn (calf) all missed the victory over the Bulldogs and are some chance of a recall this week.
One man who will be there is defender Nick Malceski, who is off contract at year's end and has put off talks over a new deal until the end of the season.
While Malceski has been linked with a number of other clubs, McVeigh is hopeful he will remain in Sydney.
"There's no harm in putting your contract talks off," McVeigh said.
"We love 'Mal' and want him to be a one-club player and play at this footy club for the rest of his career.
"He's had an injury-interrupted career and he's really hitting his form and should be an All Australian this year."
Another important member of the Swans' forward set-up, alongside Franklin and Tippett, is Adam Goodes.
The two-time Brownlow medallist has played 16 consecutive matches since returning from his own knee injury, kicking 23 goals.
McVeigh is confident the 34-year-old, who has played 347 career games, will continue on next season.
And he feels the two-time premiership winner is also hitting his straps at the right time.
"He's been going great," McVeigh said.
"We saw the footage 'Horse' (Swans coach John Longmire) showed yesterday of his running (against the Bulldogs) and it was unbelievable.
"He took on a few guys and put 15m on them and got that goal in the goalsquare, so he's still got that speed, he's still got that hunger and he's one of those players you walk taller with when you stand with them in the race."
