The Ospreys' Liberty Stadium in Swansea was a possible alternative, given it can hold just over 20,000.
But Scarlets chief executive Stuart Gallacher said: "We have made an early decision on the venue to end speculation from media and spectators that we were moving the game away from Stradey Park.
"Our players and supporters deserve the best possible opportunity of progressing further in the knockout stages, and we believe playing at Stradey Park gives us that chance."
Llanelli qualified for the knockout phase as second seeds after winning all six of their group games.
Leicester directors will also meet this week after Tigers landed a lucrative home tie against current French Championship leaders Stade Francais.
Tigers moved a 2005 semi-final against Toulouse and last season's quarter-final appointment with Bath across the road to Leicester City's Walkers Stadium, but having lost on both occasions, Welford Road would be the choice of Leicester supporters, even though it has a considerably smaller capacity.
Leicester and Stade will meet for the eighth Heineken Cup occasion, a sequence which includes an epic 2001 final in Paris won by Tigers, and head coach Pat Howard is relishing what could be an enthralling encounter.
"First of all, I am just delighted that we are into the last-eight after coming through a tough pool," said Howard, following Leicester's historic Heineken Cup victory over Munster at Thomond Park.
Leicester became the first visiting team to win a European tie in Limerick, and Howard added: "It was a great win and we were very happy to enjoy the moment.
"It has also allowed us to go another step, and now we face another tough tie, but we know we can compete against anyone."
Wasps are likely to keep their last-eight clash against Leinster at Adams Park in High Wycombe after reaching the knockout phase for the first time since being crowned European champions in 2004.
Wasps hooker Raphael Ibanez said: "We were fighting for a home quarter-final berth, and it is great to have achieved that. It will be a brilliant day, and I know our fans are already looking forward to it."
And Biarritz coach Patrice Lagisquet says his side need to improve to reach the standards they set in making the Heineken Cup final last season, despite ending the pool stage as top seeds.