Barcelona and last season's runners-up Liverpool will go head-to-head in the semi-finals - a reunion for veteran forward Suarez, starting at Camp Nou on Wednesday.
Suarez spent three years at Liverpool, winning just the EFL Cup on Merseyside, before joining La Liga giants Barca in 2014.
Under Jurgen Klopp, Liverpool
"The race is so tight in England this season it is impossible to say out of Liverpool and Manchester City who will be champions.
"But Liverpool are now in a position where they will be challenging in the future. When we nearly won the title there was so much disappointment because I think there was a feeling that was our moment and we wouldn’t get another.
"But now Liverpool have the squad, the investment, the set up where this will not be a one-off season."
Suarez, who has won four La Liga titles and the Champions League among other honours with Barca, added: "Liverpool will always be important for me - for giving me an opportunity, for playing a big part in my development, and of course for the amazing fans.
"But this is a Champions League semi-final and all that will matter is helping Barcelona fight to get one step closer to another trophy."