Bradley, the first American manager in any of Europe's five leading divisions, endured a miserable, brief reign, taking just eight points from 11 games.
"We are sorry to lose Bob after such a short period of time, " said Jenkins.
"He had that interview [in October] and missed out to Bob Bradley, so I wouldn't say that he's the favourite".
Goals from Andre Ayew, Winston Reid, Michail Antonio, and Andy Carroll secured another important win for Slaven Bilic's men, who moved up to 11th as a result of their sixth league victory of the campaign.
A 4-1 defeat to West Ham on Monday was the final straw for the Swansea City's owners who confirmed his dismissal on the club's official website. Bradley vowed to "fight like crazy" in the wake of the ugly loss to the Hammers, but admitted that his future was out of his hands.
Having conceded 41 goals already this season, more than any other club in the Premier League, Swansea would no doubt jump at the chance of signing 36-year-old Terry.
First-team coaches Paul Williams and Alan Curtis will take over from Bradley on an interim basis as the club searches for a new manager.
Shot, 11 Fatally, In Bloodiest Holiday Weekend In Years
The last weekend of mass destruction was the four-day Thanksgiving weekend, when 61 people were injured and nine killed. Gang violence has been blamed for the bloodshed on the city's south and west sides Christmas weekend.
Swansea City sacked manager Bob Bradley on Tuesday evening.
They are all chasing the huge rewards available to winners, with accountancy firm Deloitte forecasting that last season's surprise champions Leicester City, owned by Thai businessman Vichai Srivaddhanaprabha, will enjoy revenues of at least £155m in the 2016-17 financial year, regardless of this season's performances.
"You've got the January transfer window coming up and you can pick up a couple of players and strengthen the squad a bit".
"Him going there, I think he can turn it around".
Bradley, who coached (managed) three different teams (clubs) in MLS, was the US national team coach from 2006 until his firing in 2011. In all honesty, Bradley knew this was a risk and he knew that there was a good chance that he was probably going to get fired very soon.
"If I was him I would go into a league that he knows best and that is the Premier League".
Since leaving U.S. shores in 2011, Bradley has plied his trade overseas, first managing the Egyptian national team before heading on to Norwegian side Stabaek Fotball, and then French Ligue 2 side Le Havre, before landing at Swansea.