The future of head coach Guidolin is due to be discussed at a board meeting on Wednesday, with the Italian keen to prolong a spell which began in January.
And Press Association Sport understands that Guidolin's appointment is likely to be agreed following Swansea's impressive finish to the Barclays Premier League season.
Swansea were two points above the relegation zone when former Parma and Udinese manager Guidolin was the surprise choice to succeed the sacked Garry Monk.
Since then Guidolin has won seven and drawn three of his 15 games in charge, and Swansea head into the final round of Premier League fixtures this weekend on 46 points and with a chance of a top-half finish.
The 60-year-old has made no secret of his desire to extend his short-term deal, and his cause was further helped by Saturday's remarkable 4-1 win at West Ham, who are chasing a European spot.
After that game club chairman Huw Jenkins told the South Wales Evening Post: "He (Guidolin) 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.
"He has brought in a bit of common sense and a bit of simplicity, as well as experience.
"I don't think those simple things are highlighted enough in the modern world of football.
"Sometimes other things are given too much prominence and some over-analysing goes on."
Former Swansea manager Brendan Rodgers, who took the club into the Premier League in 2012, has been heavily linked with a return to the Liberty Stadium since leaving Liverpool in October.
Rodgers revealed in January that he had been approached to succeed Monk, but he told the Swansea board that he wanted to break from football until this summer.
Source: PA