"I would like to stay. Despite everything that happened, I'm happy here, on and off the pitch... and at the club they're happy with me and want me to stay," Suarez said in an interview with the Montevideo daily El Pais.
"I have a contract until 2016 and they already want to renew it for me. The coach (Kenny Dalglish) still believes in me and that's very important, especially after having been out for eight matches," he said.
Suarez received the ban and a 40,000 pounds ($63,000) fine in December after being found guilty of racially abusing Manchester United defender Patrice Evra during a Premier League match at Anfield last October.
The 25-year-old Uruguayan felt he had been the victim in the case, saying: "What hurts me is that I was at the trial and there was no concrete proof. It was simply my word against that of the other player and they believed him. That hurt me a lot."
Suarez aggravated the issue when he refused to shake hands with Evra before Liverpool's Premier League match against United at Old Trafford last month, for which the Uruguayan later apologised.
He said he was grateful for the support he received from Liverpool and from his home country including national team coach Oscar Tabarez.
"I've already played in other countries, a lot of people know me and I've shown who I am. I don't think I deserve to have been treated as I was," Suarez said.
The forward, who helped Liverpool to victory in last month's League Cup final against Cardiff City, would love to play for Uruguay at the London Olympics but was unsure whether his club would release him because the Games overlap with the pre-season.
"If we were playing the Champions (League) it would be highly unlikely they'd let me go but now we're a long way from achieving that. The (Premier League) championship starts in the middle of August, I don't know if they'd let me go. I haven't talked about it at all with the club."
Uruguay are in the Olympic soccer tournament for the first time since they won the second of their two gold medals in 1928. The London Games are from July 27 to August 12.