The 24-year-old, who despite struggling with a thigh injury scored the winner against Manchester United almost a fortnight ago, had to pull out of England's World Cup qualifiers against Moldova and Ukraine because of injury.
Sturridge has been undergoing rehabilitation at the club's Melwood training ground ever since but is not scheduled to train for the first time until Saturday ahead of the match in south Wales on Monday evening.
However, Press Association Sport understands Liverpool remain optimistic about his progress and believe the forward, who has scored in each of their opening three league matches to fire the Reds to the top of the table, has a good chance of facing Michael Laudrup's side.
Manager Brendan Rodgers is likely to make a decision on whether to include the England international, who has five goals in four appearances this season and has scored 16 in 20 matches since joining from Chelsea in January, late on at the weekend.
There is slightly better news concerning Glen Johnson, who limped off with an ankle injury against United.
Despite reports he could be out for 10 to 12 weeks Liverpool did not put a timescale on his recovery but it seems the diagnosis is more positive.
"Injury doesn't seem as bad as first thought, hopefully be back sooner than originally expected! #BetterNews," the England international wrote on Twitter.
"Thank you everyone for the 'Get well' messages."
Johnson is likely to be out for around five more weeks and in his absence Rodgers has a decision to make over how to compensate for the loss of the right-back.
England Under-21 captain Andre Wisdom came on for Johnson against United and having initially been lined up for a loan spell that prospect has now diminished.
The Reds boss also has the option of switching to three at the back as summer signing Kolo Toure, impressive in his first two matches before missing the United game through injury, is ready to return.
Martin Skrtel deputised excellently on his first appearance of the season and it would be as difficult omit him against Swansea as it would Toure.
Liverpool's strength in the centre of defence was increased by the signing late last month of Paris St Germain's Mamadou Sakho, who could be set for his first inclusion in the squad on Monday.