Jim Bentley's side have already beaten Dagenham and Redbridge, Newport County, Oxford United and Cambridge United this season, and will fancy their chances at Prenton Park, where Tranmere are yet to win this season.
Much of Morecambe's success is down the goalscoring form of veteran winger Kevin Ellison.
The 35-year-old currently tops the League Two scoring charts, averaging a goal a game, and will be aiming to continue that run against former club Tranmere, who were boosted by striker Cole Stockton's decision to sign a new three-year contract this week.
Two League Two clubs head into this weekend on the back of giant-killing performances in the League Cup.
Burton Albion currently sit two points adrift of leaders Morecambe and triumphed 1-0 over QPR in Wednesday's second-round fixture courtesy of an Adam McGurk free-kick.
Shrewsbury Town - another of League Two's unbeaten sides - also dumped out Premier League opposition by beating Leicester City 1-0.
Burton head to Mansfield Town on Saturday, while Shrewsbury host Luton Town.
Oxford - currently bottom of the league with no points - came agonisingly close to joining Burton and Shrewsbury in causing a League Cup upset, but were edged out of the competition by West Brom, who won 7-6 on penalties following a 1-1 draw.
Dagenham are the visitors to the Kassam Stadium as Michael Appleton's men look to put that disappointment behind them and kick-start their league campaign.
Portsmouth and Cheltenham Town - like Burton - are two points off top spot and face home fixtures against Newport and Hartlepool United this weekend.
At the other end of the table, Accrington Stanley's 2-2 draw against Luton last Saturday gave them their first point of the season, but they will be eager to go one better on the road at local rivals Bury.
Exeter City and Carlisle United are one point better off and face trips to Northampton Town and Cambridge.
Elsewhere, York City - unbeaten but also without a win - host Wycombe Wanderers, Southend United head to Plymouth Argyle, and Stevenage visit AFC Wimbledon.
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