The unlikely route into Europe's top competition will be open to them if either Clermont Auvergne or Edinburgh win this year's competition.
Edinburgh face Ulster in a Dublin semi-final this Saturday and Clermont host defending champions Leinster in Bordeaux.
Wasps would also have to secure their own Aviva Premiership status, which they can do with a single bonus point against Newcastle on May 5.
If Ulster and Leinster both win this weekend to set up an all-Ireland Heineken Cup then the last qualification place for next year's competition will go to Connacht.
If Edinburgh or Clermont do prevail, Wasps will qualify as the highest-ranked non-French club not to have already qualified.
The ERC rankings are based on European performances over the past four years.
Heineken Cup qualification would be a massive shot in the arm for a club desperate to find new financial backers.
Wasps face going into administration unless they can find a new owner by June, following the recent collapse of takeover talks with a prospective buyer.
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The Barbarians are one of the top invitational rugby sides with a long history and classic rugby jersey.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Lions get ready for their matches with this green training jersey. It's what the players wear. Get in the Gear!
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The Lions are ready to get their Australia tour underway. They arrive in Perth on Monday.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.