The playoff round of the CL is split into two halves: the Champions Route, for clubs that won their leagues, and the League Route, which includes Villarreal.
There will be ten teams in the League Route playoff; five enter at that point, five are the winners of the preceding round.
The top five of those clubs (in terms of UEFA coefficient) will be seeded--so they play the second leg at home. Here is a look at where we currently stand:
The first two qualifying rounds don't matter to us, as the teams surviving from those matches move into the Champions Route section of the third qualifying round. It's the teams making up the League Route portion of the third qualifying round that interest us. Here they are: clubs with higher coefficients than ours are shown in bold.
Shaktar Donetsk, Ajax Amsterdam, Steaua Bucharest, 3rd in France (Monaco or Nice), 2nd in Russia (could be Zenit, Krasnodar or Rostov), Andelecht, Young Boys, Fenerbahce, a Greek team (could be one of four, all below us), and our new friends Sparta Prague. These teams are drawn against each other.
Then, the five winners of those matches progress to the playoff round. The teams entering are Porto, Man City, Borussia Munchengladbach, VILLARREAL, and the third-placed team in Italy. This latter is key. Napoli currently lead Roma by two points in the race for second place. Napoli host Frosinone in their last match of the season, while Roma are away to AC Milan, who have nothing to play for. (Roma owns the tiebreak by virtue of a win and a draw against the southerners).
If Roma finish second and bump Napoli to third, then Napoli, Porto and Man City would all be seeded clubs in the playoff round. If both Shaktar Donetsk and Zenit St Petersburg also progress to the playoff round, then those five clubs would be seeded and Villarreal would have to play one of them in the playoff round.
If, however, Shaktar loses its third-round qualifying match, Napoli finishes second in Serie A, or Zenit fails to finish second in the Russian league (they are currently two points behind Rostov with three matches left, and Krasnodar are two points below Zenit), then Villarreal would become a seeded team.
The difference is huge--possibly playing Napoli, Man City, or Porto just to get into the CL group stage is not something we would look forward to. Napoli can do is a big favor with a win over Frosinone this Saturday.
NB--I have used the club coefficients calculated by Bert Kassies on his website, which show Villarreal at at least 60.028 and Ajax at 58.112. The official UEFA website shows Villarreal at 57.685. I have confirmed with Mr. Kassies that his calculations are up-to-date and Villarreal is indeed ahead of Ajax!