Sanchez is available on a free transfer after his contract with Valenciennes expired and Bolton had been favourites to sign the Colombia international.
Coyle had been hopeful of concluding a deal for the 26-year-old, who would help to fill the void created by Nigel Reo-Coker's departure from the Reebok Stadium.
However, Coyle says the player's demands changed following further talks and he has now decided against adding Sanchez to his squad.
"He's a player we enquired about a couple of months ago, and in between that, I was on holiday and Phil (Gartside) did meet with his representatives," Coyle told the Bolton News.
"At that point, they thought they were close to a deal and then their demands changed.
"Again last week, I had another email to say he was coming over, and to be fair, I think he did manage to get into the country but the next email with the demands was absolutely ridiculous.
"A couple of months ago, we'd written it off anyway and they seemed to come back on and try and get us back involved.
"There was no point meeting with the player because of the demands they had put forward. They were far and away beyond our means, and I've got to say, they would be out of the reach of a lot of top-six clubs as well.
"If I thought it was realistic, then he's a good player and he's the type that would add to our squad because he's a holding midfielder and that's the kind we need at the moment.
"He (Sanchez) is that quality but the money he was asking for surpasses even that."
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