The Spaniard, who has been linked with a return to the Premier League, is reportedly among the candidates for the role at Stamford Bridge.
Alonso has been without a job since being dismissed by Real Madrid in January after only seven months in charge.
For the former England international said that while the Spaniard remains one of football’s brightest young managers, Chelsea’s recent instability should serve as a warning.
“Pretty much. I think the Liverpool people would give him time. But as we've seen, if he had that role, the Chelsea fans might not be so...,” Johnson told GOAL.
“We know that the manager will see that Chelsea is probably the hottest seat in world football. It's hard for a young manager to go there knowing that you don't have six months, you don't have a year, you definitely don't have 18 months.
“So you've got to go through that door and win immediately, and that's hard for, as proven, top managers that have won stuff. That's almost impossible for anyone to do. I think it'd be a crazy seat to take for a young new manager, as we've just recently seen.”