Representatives of Sanchez have held talks with Liverpool over a possible move to Anfield in part-exchange for Suarez, who is expected to seal a move to the La Liga giants within days.
But sources said the Chile international, 25, had decided against joining Liverpool, with reports suggesting that Arsenal were now the favourites to sign him ahead of Juventus and AC Milan.
Barcelona and Liverpool both valued Sanchez at 30 million pounds, which would have made him a makeweight in the deal for Uruguay international Suarez.
The sale of Suarez will still go through, with a basic framework for a 75 million pound deal in place, although the two clubs have yet to sort out a payment structure.
Suarez is serving a four-month worldwide ban imposed by FIFA after he bit defender Giorgio Chiellini during Uruguay’s 1-0 World Cup Group D victory over Italy in Natal on June 24.
It means that, if an appeal by Uruguay’s football association, the AUF, is unsuccessful, he will be unable to play until late October.
Liverpool are continuing to pursue deals for Benfica’s Serbian winger Lazar Markovic and Lille’s Belgian forward Divock Origi.
They are also chasing Southampton’s Croatian centre-back Dejan Lovren, while they have not given up hope of signing Sevilla left-back Alberto Moreno.