Bielsa's current deal expires in June.
Beckford said, "They could be successful under another manager, but I want Bielsa to stay. Radrizzani wants Bielsa to stay, everybody connected to Leeds United wants Bielsa to stay, every neutral would like Bielsa to say because it's given Leeds United a whole new meaning.
"I love Leeds, I love what he's done with Leeds and I love the feeling you get watching Leeds United, as a neutral or as a huge fan and he's done that, he's brought that to Leeds United, he's - to an extent - brought the glory days back. Everybody is thrilled when Leeds are on television.
“If we're being honest with ourselves, when he took over Leeds United, they were a mid-table Championship side and that's no disrespect to them. The players there were doing really, really well with what they knew and what they had at the time, to their disposal.
"Bielsa came in and the first season he came in, he completely changed the whole philosophy of the whole team; the style of play, the intensity that the players trained at and played at. It was beautiful to watch, the very first game in the Championship after he took over and now we've seen that after two and a half, almost three years, and we've bought into it and he's bought into it.
"He's bought into the city of Leeds, he's bought into the football club, he's bought into everything connected with it and as a Leeds United fan, we don't want to see him leave."