The Swans sat in the relegation zone when Guidolin was confirmed as their manager until the end of the season, and the Italian has since steered them comfortably to safety in the Premier League.
"We have got our normal monthly board meeting on Wednesday and, yes, we will be discussing the managerial situation. We are talking things through this week and we will give out a further update when we can. It could be this week or it could be next week when a decision is made," Jenkins told the South Wales Evening Post.
"There's lots to talk through. We will talk about the season we have had, where we have finished and what we feel we need in the summer. [Guidolin] has brought exactly what he thought he would bring to us," said Jenkins. 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 manager Brendan Rodgers has been heavily linked with a return to the club should Guidolin leave this summer.