The Tigers must decide what happens next after boss Marc Richards left the club to take over at National League North Hereford.
Until a replacement is found, experienced Webb and Green will look after the team.
Chairman Rod Jenner has confirmed assistant manager Will Morford and performance analyst Luke Brick will also be leaving for Edgar Street.
“We are of course very sad to see Marc, Will and Luke leave the club, however, Marc feels that it is time to move to pastures new,” Jenner said.
“I would like to thank him and Will for the job that they have done these past ten months. I’d like to especially thank Will for stepping up and taking charge of the first team for those few games in December last year.
"On behalf of the directors, management board, and all those involved with the club, I want to wish them all the best for the future.
“My role as chairman means I must protect the club’s best interests, so when Marc informed us of his intention to discuss this new opportunity, the management board and I set about contingency plans in case this scenario happened.
“Our proactivity has been justified and we’ve already identified a number of candidates who we will be interviewing soon.”