Steven Gerrard (PA Photos)
Gerrard, who made his debut for the Anfield side in 1998, has insisted he was the subject of a bid from an unnamed European club last season which the Daily Telegraph reveals was Bayern Munich.
Bayern went on to win the treble of Bundesliga, Championship League and German Cup while Liverpool finished seventh in the Premier League and without a trophy.
Gerrard told several national newspapers: "I had a chance to leave last year. It was for a club in the Champions League, not a Premier League club, but I wasn't tempted. I've been through that before."
Gerrard, once a target of Premier League rivals Chelsea, wants Suarez to stay despite two bids from Arsenal.
However, the England midfielder admits until they regain their top-four place they will always have to fight such battles.
Speaking ahead of Saturday's testimonial against Olympiacos, Gerrard said: "I think the only person who knows what's happening is Luis himself.
"He has a huge decision to make and, as his team-mate, I have to show him respect and give him space to make whatever decision he wants to make.
"But I think everyone knows how highly I rate him and how much I want him to stay, and what we can achieve this season basically depends on whether he stays or goes, I believe.
"While I've still got a couple of years left - and maybe a few more - I have to make the most of it. And that is about adding more medals to what I already have and to leave this club in the Champions League. That is the challenge for me personally.
"It is not the same club (I joined) because we are not in the Champions League, so it becomes an awful lot more difficult to attract the top players.
"But I think the club's history and size - we've just been on a tour which has seen us play in front of nearly a quarter of a million people in 10 days - means the pull is still here.
"We need to break back into the top four to get back the pull we had four or five years ago when we were comfortably in the Champions League year in, year out and challenging to win it.
"Players who come and get the club back into the Champions League will experience some of the biggest nights of their career, because playing European football in front of this crowd is different to any other."
Eurosport / PA Sport