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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