Redknapp's men eventually finished the 2011-2012 season in fourth in the Premier League, while it reached the FA Cup semi-finals.
Then linked with the England job, the 69-year-old said Tottenham was close to signing Suarez and Hazard.
"I was managing a Tottenham team I thought could go on and win the title, I genuinely believed that," Redknapp told talkSPORT.
"We got Louis Saha and Ryan Nelsen on free transfers – we were short, we had injuries at centre-half and I had no striker.
"If we had gone out [and invested] then, Luis Suarez was the player we were looking at."
Suarez joined Liverpool in January 2011, scoring 69 league goals in just 110 appearances for the club.
Another player Redknapp said he was close to signing was Hazard, who joined Chelsea in mid-2012 and has won a Premier League and Europa League with the club.
"I met Hazard and spent three hours with him in a hotel in Paris – I met him at the airport and he was dead keen to come to Tottenham," he said.
"We were right down the road with Hazard and Luis Suarez was the best player in the Premier League when he was at Liverpool, he was fantastic.
"If we just got one of those in, we had a team that could have challenged for the title."