There is one rather pointed clue in Half-Blood Prince, when Lupin visits the Weasleys for Christmas.
Meanwhile, Remus Lupin, who was thinner and more ragged-looking than ever, was sitting beside the fire, staring into its depths as though he could not hear Celestinas voice.
Oh, come and stir my cauldron,
And if you do it right,
I'll boil you up some hot strong love
To keep you warm tonight.
Men staring deeply into a fire while a love song plays generally only means one thing.
More to the point, when he tries to talk Tonks out of a relationship, his excuses are varied.
"And I've told you a million times," said Lupin, refusing to meet her eyes, staring at the floor, "that I am too old for you, too poor... too dangerous..."
"I am not being ridiculous," said Lupin steadily. "Tonks deserves somebody young and whole."
If he didn't want to date Tonks because he doesn't like her, surely that would top the list? But his response seems to take for granted that if he were young, whole, safe, etc., they would be together. I don't see how to take that other than an admission he has feelings for Tonks. And if he did lack feelings for Tonks, Lupin doesn't seem like the type to torture her for months by leading her along.
More to the point, people don't generally become a couple and then married in the span of a month. I think it's clear they were deeply in love.