Rodgers was linked with the Swans after being sacked by Liverpool in October.
"There were talks with Brendan, and with one or two other people, but that is just us doing our jobs and seeing where we go with that," Jenkins said.
Italian Guidolin took over in January and has agreed a deal to stay until the end of the 2017-18 season.
Jenkins said Rogers, who guided Liverpool to second place in the Premier League in his second season in charge, was an "obvious option".
But he added: "We had to make a decision based on what we felt was right at the time. Timing is a big one.
"We are going through a period where Francesco Guidolin is doing a good job and has just helped us to probably a mid-table finish in the Premier League, again."
Jenkins said Guidolin's appointment had the "unanimous" backing of Swansea's board and confirmed the club plans to keep the 60-year-old's backroom staff in place.
The chairman described this season, which saw Garry Monk sacked in December with Alan Curtis taking over as caretaker until the appointment of Guidolin, as "a challenge".
"We didn't hide away from it, we knew what we had to do," said Jenkins.
"Some people would say we should have done it sooner - but we got to grips with things that needed to be changed.
"We needed to get back to playing football the right way and we managed to do that, first with Alan Curtis and the staff and then Francesco added more experience.
"Perhaps the squad of players who were criticised early on in the season have proved they are a good squad.
"I am pleased for them as well. They have shown they can play, they have come through it and shown a good standard by the end."
Swansea held talks with ex-boss Brendan Rodgers before Francesco Guidolin signed a two-year extension to remain in charge, says chairman Huw Jenkins.