Monk took training as usual with the team on Tuesday but Jenkins - in London to collect his OBE for services to sport in Wales - indicated an announcement on his future could be imminent.
Jenkins said: " "We all feel at the club that something needs to change to get things back on a positive note as quickly as possible and get us back to the levels of performances we have got to have to win games at the Premier League level."
Jenkins refused to confirm whether Monk would be sacked, but asked if an announcement would be made on Tuesday, replied: "Not today, because I am up here [in London]."
Swansea have won once in their last 13 games and Saturday's 3-0 home defeat by Leicester left them just one point above the Premier League relegation zone
Monk survived showdown talks with Jenkins on Monday but his departure now seems just a matter of time with Brendan Rodgers and David Moyes among those strongly linked with the Liberty Stadium post
Monk guided the Swans to an eighth-place finish in the top-flight last season but their form has nose-dived during this campaign, prompting Jenkins to admit major changes are necessary
Jenkins added: "The difference between the end of August and how we find ourselves today is something we haven't experienced at Swansea before, such a big change around from where we were after beating Man United in the last game in August
"I think it just again highlights if things are not dealt with and addressed early enough the Premier League is very unforgiving, and unless every angle and everybody's focus is 100% week in, week out, things can change very quickly."
Source : PA
Source: PA