Suarez, 34, enjoyed a four-year spell at Anfield from 2010-2014 and scored 82 goals in 133 appearances.
The striker almost led the club to the league title in the 2013-14 campaign but they finished in second place behind eventual champions Manchester City.
The Uruguay international said he is happy that Liverpool managed to secure their first Premier League title in 2019-20 but added he is not considering a second stint in England.
"Playing for any team other than Liverpool in England would be hard," he told World Soccer Magazine.
"I had, and hope I still do have, such a good relationship with Liverpool fans that it would be strange for me to play for somebody else.
"It would have been special to win the league with Liverpool, but I am glad that their wait is now over.
"They look like a team that will compete for many seasons to come even if this one has not been the best for them. They are back where they belong."
Last season, Suarez played an integral part in helping Atletico claim their first La Liga title since 2014.
The striker moved to Atletico from Barcelona on a free transfer and contributed 21 goals in all competitions, including the winning strike in the final day victory at Real Valladolid that clinched the title.
When asked about his future at the club, Suarez replied: "At the moment I am enjoying my time here. I enjoy it here, we are settled in Spain -- there is no need to think about me leaving
"When I think how well I have settled in at Atletico and the faith the coach has shown in me, it was easily the right decision for me."