Johnson reckons the other three London clubs - Harlequins (11th last season), London Irish (eighth) and Saracens (fifth) - should start the new campaign believing they can make one of the top-four spots.
He added: "Everyone needs a bit of luck with injuries and you have to be playing well the whole year to stay in the race. But there are other clubs apart from Leicester who will think they can do it.
"Quins underachieved last year, but they came through in the second half to win the European Shield and were runners-up as well in the Tetley's Bitter Cup to Newcastle at Twickenham.
"They have since made some important signings with players like Danny Luger and Bill Davison back in the club and Tony Diprose joining them for the first time.
"They are good enough for the top four in the Premiership, they know that, but they also have the talent to compete for all the trophies.
"The Irish have signed a couple of Southern Hemisphere players, as usual, and it is worth remembering that one of them - Brendan Venter, who is their player coach now - was a big influence on them when he was with them before in midfield.
"The first time we won the league at Leicester, the Irish were one of the best of the opposition and they beat us at home when they were playing at Sunbury, so if they find some of that spirit they could go very well.
"Saracens have lost some players and have some injuries, but I still believe that they are a team to be reckoned with.
"They have been one of the closest rivals we have had at Leicester in the pro era, we have had some great games with them and we have to remember that we have not won at Vicarage Road for three years.
"Even if Saracens have some problems, they remain a good side."
