Guidolin is under pressure with the Swans only one point above the relegation zone.
Swansea's American owners, Steve Kaplan and Jason Levien, have yet to decide on Guidolin's future.
However, they are compiling a shortlist of potential successors to the Italian.
The owners will be in attendance at the Liberty on Saturday.
Chairman Huw Jenkins has met former United States coach Bob Bradley, while former Wales and Manchester United captain Ryan Giggs would be interested in the manager's role if it was to become vacant.
Bradley and Giggs are not the only options, with Swansea's hierarchy thought to be considering several other possible candidates in the event of Guidolin's departure.
Any decision on Guidolin's future will be taken jointly between Kaplan, Levien and Jenkins.
They have become concerned in recent weeks, with Swansea failing to win in the Premier League since their opening-day triumph at Burnley.
It is understood the nature of the Swans' performances in their next few games - a trip to Arsenal follows the Liverpool fixture - will have as much of a bearing on Guidolin's future as the results.
The 60-year-old succeeded Garry Monk as Swansea boss in January and, after guiding the Welsh club to Premier League safety last season, the former Udinese manager was rewarded with a two-year contract in May.
Guidolin insists he still has the support of the players and he has not sought assurances from Jenkins about his future.
"I spoke with the chairman last week," he said.
"But at the moment the most important thing is for me to work with my players and with my team to prepare for the next game, to be focussed and with concentration."
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Swansea are four points clear of the relegation zone after a much-needed 2-1 win at Everton.
The Swans had beaten Watford earlier in the week and Williams wants the team to continue the momentum.
"The main thing is we build on it and that was my message before the game," Williams said.
"We want to put a run together now and pick up as many points as we can to put a bit of distance between ourselves and the drop zone.
"Every team has a little run, whether it's a good one or a bad one, throughout the season.
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"We'll try and make it our turn to have a good one now."
New head coach Francesco Guidolin's first game in charge saw Swansea secure a first ever league win over Everton and two successive wins for the first time this season.
Wales defender Williams has been impressed by the Italian, who previously coached Udinese and Monaco.
"He's lifted the place a bit and also tried to implement some of his own ideas into the team in the week," Williams added.
"He wants us to play our own game with a few little tweaks and ideas that he thinks will help us.
"I look forward to working with him and all the lads have been impressed with his first week and the way he goes about work and what he's asking of us.
"It looks good at the minute. It's been a good week for us and now we can settle down again, collect our thoughts and go again."
Swansea's next Premier League game on Tuesday, 2 February will be away to the side immediately above them in the table, West Bromwich Albion.
Francesco Guidolin's future as Swansea City head coach will not necessarily rest on Saturday's Premier League match against Liverpool - even though the Italian admitted it could be his last.
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Captain Ashley Williams has challenged Swansea City to maintain their winning form following back-to-back wins in the Premier League.