Allen is named in the centres for the first time since September having recovering from a thumb injury, while Parling starts at lock after five weeks on the sidelines.
Allen comes into the side for the injured Toby Flood, with Billy Twelvetrees switching to the No.10 jersey - however Manu Tuilagi and Louis Deacon among those also missing.
As a result Boris Stankovich, George Chuter and Tom Croft have been handed recalls.
Struggling Wasps have made four changes as they look to end a five-game losing run in the Premiership.
All the changes come in the back division, with Hugo Southwell, Richard Haughton, Nic Berry and Ryan Davis all handed starts. Southwell's return from injury means Elliot Daly switched to outside centre.
On the bench, on-loan Mike Powell, who has joined from London Welsh as cover for the second, and Jack Wallace both earn call-ups.
"We know we are facing one of the league's in-form sides but we won't be lacking in motivation going up there as the players really want to turn around their fortunes after a few disappointing results," said director of rugby Dai Young.
Leicester Tigers: 15 Geordan Murphy (c), 14 Horacio Agulla, 13 Matt Smith, 12 Anthony Allen, 11 Alesana Tuilagi, 10 Billy Twelvetrees, 9 Ben Youngs, 8 Thomas Waldrom, 7 Julian Salvi, 6 Tom Croft, 5 Geoff Parling, 4 Steve Mafi, 3 Dan Cole, 2 George Chuter, 1 Boris Stankovich.
Replacements: 16 Rob Hawkins, 17 Julian White, 18 Logoviii Mulipola, 19 Ed Slater, 20 Ben Woods, 21 Sam Harrison, 22 Jeremy Staunton, 23 Scott Hamilton.
London Wasps: 15 Hugo Southwell, 14 Tom Varndell, 13 Elliot Daly, 12 Riki Flutey, 11 Richard Haughton, 10 Ryan Davis, 9 Nic Berry, 8 Sam Jones, 7 Jonathan Poff, 6 Tinus Du Plessis, 5 Marco Wentzel (c), 4 Richard Birkett, 3 Ben Broster, 2 Rob Webber, 1 Tim Payne.
Replacements: 16 Tom Lindsay, 17 Bob Baker, 18 Jeremy Castex, 19 Mike Powell, 20 Matt Everard, 21 Joe Simpson, 22 Jack Wallace, 23 Chris Mayor.
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