The Merseyside outfit are in sixth place and six points behind fourth-placed Manchester City, who occupy the final Champions League qualifying spot.
The Reds have won their last three Premier League games after scoring 11 goals in victories over Aston Villa, City and Crystal Palace in the past few weeks.
City, Manchester United and West Ham are all contenders for a top-four finish.
But former Liverpool midfielder Garcia believes Chelsea could prove the toughest rival for a spot in next season’s Champions League.
“We’re in that moment when you don’t know if they’re going to reach the Champions League, it’s getting far away. “Chelsea is recovering and they’re going to be another contender to fight for those four or six positions,” Garcia told Omnisport.
“Liverpool needs to be there for next year. I think it’s very important because the top players want to play in the Champions League and if you are not there, they don’t think about coming. It’s difficult of course, but we knew that from the very beginning.
“Now Sturridge is getting fitter, Coutinho came back from an injury and Firmino has been scoring goals. I think the team is looking better and hopefully they can get those two or three wins in a row and close the gap on fourth position.”
Enhanced odds: Get 7/1 on Liverpool to beat Man Utd
Liverpool appointed Klopp as their manager in October after Brendan Rodgers was sacked.
The Reds will host Manchester United in the first leg of their Europa League last-16 clash at Anfield on Thursday night.
Liverpool make the return trip to Old Trafford on 17 March.
MORE: Latest Man Utd news
MORE: Latest Arsenal news
MORE: The latest football news