The Welsh club were set to reunite with former boss Rodgers, but have had a change of heart in recent weeks and will offer Guidolin a new deal.
The Swans only appointed Guidolin on a short-term deal until the end of the season in January after sacking Garry Monk the previous month.
Though the Portuguese boss has an inauspicious start to life in South Wales, he appears to have begun to have an impact at the Liberty Stadium in recent weeks, with results noticeably improving for the club.
Swansea, who were in the relegation zone when Guidolin took charge, have lost just five of their 15 Premier League matches under the 60-year-old's rule, and have won six of the last 10.
That form has seen them avoid any serious relegation danger by moving from 18th up into 11th with just a game to go, and it seems as though the improvement has been enough to convince chairman Huw Jenkins and the board that he is the right man to lead the club next season.
The Telegraph claims that Swansea had previously held talks with Rodgers, the man who guided them to promotion to the Premier League in 2011, over a potential return.
However, the recent back-to-back wins - a 3-1 victory over Liverpool before a 4-1 thrashing of European challengers West Ham United at Upton Park last weekend - appear to have convinced the board to perform a U-turn and instead extend Guidolin's stay.
Jenkins is quoted by the Telegraph as saying: "He has brought exactly what he thought he would bring to us. He has adjusted in his time here — he has got to know the squad and got used to the Premier League.
"We have got our normal monthly board meeting on Wednesday and yes, we will be discussing the managerial situation. We will talk about the season we have had, where we have finished and what we feel we need in the summer."
Rodgers, who was sacked by Liverpool at the start of October, had been hoping to make his return to management at his former club, but will not have to look elsewhere.
His name has cropped up high on list of potential candidates to replace Ronny Deila at Celtic, and despite his troubles at Liverpool his record at Swansea and Watford are likely to make him a strong candidate for a host of clubs.