Where are Littlefinger's ultimate loyalties? Not with the Baratheons, the Arryns, nor the Lannisters.
The Baelishes claim to nobility only goes back a few generations, iirc. Who raised them to nobility? Either the Arryns or the Targaryens. We know that Petyr murderd Jon and Lysa Arryn and now holds their son.
The Baelishes were dirt poor with no connections, how was it that Petyr was fostered with Hoster Tully, one of the great lords of the realm? Either the Arryns, Baelishes, or Targaryens arranged it. It seems to me that the Targaryens raised the Tullys from average nobility to one of the seven great houses.
When Petyr fell in love with Catelyn, who prevented him from courting her? The Starks. The Targaryens killed Rickard, Brandon, and Lyanna Stark... no doubt this pleased Littlefinger.
We now know that Lord Baelish 1) got rid of Jon Arryn, 2) attempted to frame Tyrion Lannister for the attempted murder of Bran Stark, 3) tried to prevent Robert from having Danaerys Targaryen assassinated, 4) permitted, if not assisted in the death of Robert Baratheon, 5) betrayed Ned Stark, 6) worked against Stannis' and Renly's attempts to gain the throne, 7) sold out Joffrey to the Tyrells, 8) kidnapped Sansa Stark, the heir to Winterfell, 9) stole custody of The Vale, and 10) is working on the downfall of Cersei Lannister.
Why is he doing all of this? He hates the Starks, he's betrayed the Arryns, he's denied the Baratheons, he's betrayed the Lannisters, he's betrayed the Tullys, he's done nothing for or against the Martells and Greyjoys, he's assisted the Tyrells (I'm sure for an unnamed price), and yet he's helped the Targaryens for free.
Could Littlefinger secretly be a Targaryen loyalist or is he doing all this for himself?
The two most clever councillors to the realm are/were Littlfinger and Varys. Each publicly and privately admitted to despising the other. But I assume the Varys is dedicated to the return of House Targaryen, so perhaps the two sneakiest members of the Small Council were actually in alliance.
Perhaps Littlefinger is doing all this for himself. If he assists Dany in her return, he'll expect rewards. If Dany is still unmarried, she'd need to take a husband from among her subjects to help insure their loyalty. The Lord of Harrenhal and the (adoptive) father of the Lord of the Vale might be a match for the queen... if she married a son of one of the great houses, then the others would be very jealous and suspicious.