Partners are currently voting on who will fill the supervisory and ambassadorial role from May 2010.
Jenkins, who is also head of international development at Eversheds, is up against head of international litigation and dispute management John Heaps, transport head and former London head Cornelius Medvei and property partner and Cardiff head Alan Meredith.
Jenkins became chairman of the firm in 2004, taking over from Keith James. He was reelected in 2007 in an uncontested election.
The firm recently changed the rules governing the chairman’s term, extending it from three to four years and limiting the number of terms each chairman can occupy to a total of two.
Each partner has one vote and the single transferable voting system will be used in an election that will be conducted by Electoral Reform Services. The result will be announced by the firm’s appointments committee before the end of February.