Arch-rivals Manchester United stand between them and a place in the last 16 this weekend.
The Reds secured their place in next month's Carling Cup final earlier this week and are now targeting more success in knockout competition against United at Anfield.
Gerrard, speaking after the aggregate win over Manchester City on Wednesday, told www.liverpoolfc.tv: "We've got to dust ourselves down and get our recovery in because in just over 48 hours we've got a massive game in the FA Cup and we want to do the same in that competition - we want to go a long way."
The clubs have won the FA Cup 18 times between them, and United hold the edge in meetings between these teams in this competition, having won nine of the 16 previous encounters.
Their recent record against the Merseysiders at Anfield is less impressive however, having drawn there in the Premier League in October after losing on their three previous visits.
It will be the first meeting of the sides since Liverpool striker Luis Suarez racially abused United full-back Patrice Evra, an offence which subsequently earned the Uruguayan an eight-match ban that rules him out of the tie.
Controversy also surrounds the west London derby between QPR and Chelsea, which is set to bring together Rangers defender Anton Ferdinand and Chelsea counterpart John Terry for the first time since Terry was accused of racially abusing Ferdinand during the Premier League game between the sides at Loftus Road in October. Terry faces a criminal charge over the incident and denies any wrongdoing.
Tottenham make the short trip to Watford in one of two ties to be played on Friday night, with the other Friday match an all-Premier League affair between Everton and Fulham at Goodison Park.
Kazenga LuaLua could return from injury to face his former club when Brighton host Newcastle in the Saturday evening match.
LuaLua, who joined the Seagulls permanently in November following three successful loan spells on the south coast, is back in training having spent three weeks out with a hamstring problem.
League Two side Swindon, who created one of the few third-round upsets when they knocked out top-flight Wigan, travel to big-spending npower Championship club Leicester aiming to spring another surprise.
Bolton are at home to Swansea and West Brom host Norwich in two more all-Premier League ties on Saturday.
Elsewhere, Blackburn host Sheffield Wednesday, whose city rivals Sheffield United are at home to Birmingham. Stoke travel to Derby, Hull host Crawley, Millwall face fellow Championship club Southampton at St Mary's and Stevenage take on Notts County in a tie which ensures a League One presence in the last 16.
Sunderland are at home to north-east rivals Middlesbrough in the first of Sunday's games, with Arsenal taking on Aston Villa at the Emirates Stadium later in the day.