yes he could have, trial by combat was a solution that little finger could have chosen  . as there was no true evidence on his crime and all the starks had was bran's visions and Sansa's association with half his crimes. none of them was half as good as the evidence against Tyrion in his trial, and after all, he was a noble-born with all the right to ask it

but he knew it would be a bad idea for a simple reason .. according to the Westerosi traditions unless you are a woman, a person with a disability, or a member of the royal family you can't have a champion to fight your battles.

if baelish chose a trial by combat he would have had to carry a sword and fight any champion Sansa would choose to take him out making it a suicidal move for a man with his non-physical skills

or he could overcomplicate the situation and pull a ser Dunkin the tall by asking a trial of seven as having other 6 good knights by his side could even the odds but even a man with half little finger intelligence would know that none of the knights of the vale even those who don't despise him would risk his life in such one of a century trial known with its dangers and Sansa wouldn't give him a time or chance to hire sellswords that reside the closest south of the neck

so he chose to play it the only way he knows how and tried to manipulate Sansa one last time by trying to get her sympathy. it was a desperate move that for the last second believed it would work, it didn't but at leased gave him a quick death. something he wouldn't have gotten if he chose to ask for a trial

Yes he could have. Trial by combat was a solution that Littlefinger could have chosen. As there was no true evidence on his crime and all the Starks had was Bran's visions and Sansa's association with half his crimes. None of them was half as good as the evidence against Tyrion in his trial, and after all, he was a noble-born with all the right to ask it.

But he knew it would be a bad idea for a simple reason: according to Westerosi traditions unless you are a woman, a person with a disability, or a member of the royal family you can't have a champion to fight your battles.

if Baelish chose a trial by combat he would have had to carry a sword and fight any champion Sansa would choose to take him out making it a suicidal move for a man with his non-physical skills

Or he could over-complicate the situation and pull a Ser Dunkin the Tall by asking a trial of seven as having other 6 good knights by his side could even the odds but even a man with half Littlefinger's intelligence would know that none of the knights of the vale - even those who don't despise him - would risk his life in such a once of a century trial known with its dangers and Sansa wouldn't give him a time or chance to hire sellswords that reside the closest south of the neck.

So he chose to play it the only way he knows how and tried to manipulate Sansa one last time by trying to get her sympathy. It was a desperate move that until the last second he believed it would work. It didn't but at least gave him a quick death, something he wouldn't have gotten if he chose to ask for a trial.