The Magpies are set to make the 31-year-old England international the first signing of Saudi Arabia’s Public Investment Fund consortium since their takeover last year.
Newcastle have agreed a £12m fee with the Spanish champions and Trippier is already in England undergoing a medical.
The former Burnley defender joined Atletico Madrid from Tottenham Hotspurs in the summer of 2019 and has made 86 appearances in total for the club, including 15 in La Liga this season.
Trippier helped Atletico win La Liga last year.
"I always look at the positives," Simeone said at a news conference on Wednesday previewing Atletico's Copa del Rey round-of-32 tie with Rayo Majadahonda.
"I'm absolutely grateful for the time Kieran has been here with us. The club gave him 48 hours to resolve the situation. He's behaved very well and been very important for us."
"We look ahead to what is next, and seek out alternatives," he added. "The club knows exactly what we need and are after.
"We are always in common agreement, but if not then we will continue with the players we have."
Trippier has won 35 caps for the England national team.
