The Welsh side have gained a reputation over the past few years for a posession-based style of football which has often been compared to the playing style of Spanish giants, Barcelona.
The Swans' three previous managers, Roberto Martinez, Paulo Sousa and most recently Rodgers all had a similar footballing philosophy which encouraged the passing and movement now associated with the side.
Jenkins told Sky Sports: "The way we play, the philosophy in our club is not going to change.
"We have got to bring someone in who is going to complement that.
"They have got to agree to work within our structure. Brendan did that, everything was set up for him and he continued that, built on it, and obviously we are going to continue on the right path and find the right person who is going to suit us."
Jenkins is reported to be considering Graeme Jones, Robert Martinez's assistant during his time at the Liberty Stadium, as the next man to take over at the club.