Malky was appointed as Brendan Rodgers' replacement at Vicarage Road earlier this month and Jenkins, who was a revelation in the heart of the Hornets' midfield last season, expects to get on just fine with his former team-mate.
He told the club's website: "I've known Malky a long time and I know how he works. We have a very good relationship.
"Malky's got two different styles, because he was a pretty tough guy as a player and he has that side to him but he can also incorporate the style of play that we played last season. I hope this mixture results in a successful season for us."
"To keep going with the momentum that we had last season would be a great way to begin the campaign and then we'll just build on from there."