Warwickshire had recently sacked their head coach Jim Troughton after a review into their disappointing season and earlier this month it was reported in the media that Saker, who lived near Birmingham when he was England's bowling coach and had previously been linked with the role, had contact with the club in recent weeks.
However, according to sources in Sri Lanka Cricket (SLC), Saker will stay with the Sri Lankan team.
"We have lots of international tours coming up and being associated with the national side can give him an opportunity to be the head coach in the future," sources said.
The English county has advertised for a first-team coach on its and the England and Wales Cricket Board websites. Applications close today (14) and then an interview process will begin.
Meanwhile, all Sri Lanka national players (and support staff) chosen for the training camp reached Kandy on Friday.
"They assembled at the SLC headquarters in the morning and left for Kandy at 11 a.m. All were recently tested for Covid-19 and results came back negative," a source attached with the team management said.