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Saturday's loss to Liverpool was the Swans' third in succession, leaving them a point above the bottom three and increasing the pressure on Guidolin.
Although they are alarmed by the club's predicament, Swansea's owners are understood to have no immediate plans to sack the 60-year-old Italian.
"I am sure in the future this team can turn this situation," said Guidolin.
"The relationship between my players and me is perfect. The best thing in these nine months is to meet my players. I am sure they have good qualities, good character.
"I am worried for the table, not my position. It is not good. We need more points."
Swansea's American owners, Steve Kaplan and Jason Levien, were at the Liberty Stadium for the Liverpool game, but have yet to decide on Guidolin's future.
However, they are compiling a shortlist of potential successors should they sack the Italian.
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.
It is likely the nature of Swansea's performances will have as much bearing on Guidolin's job prospects as the results, and the Swans were much improved against Liverpool.
Guidolin, however, is in the dark about his future.
"I don't know what happens tomorrow, or next week," he said.
"My job is to work with the players and prepare the team for games. This is my job. I don't know if the next games brings."
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Swansea City head coach Francesco Guidolin believes his side can haul themselves out of relegation danger.