Lampard is expected to be announced as the new Chelsea manager this week.
The 41-year-old is the Blues’ all-time leading goalscorer and a firm favourite with the Stamford Bridge faithful.
But Ogden says that will not make a difference if results do not go well in his first season in charge.
And he claims Chelsea will not think twice about sacking Lampard before the end of his first campaign, as they did with previous boss Luiz Felipe Scolari and Andre Villas-Boas.
“I think with Frank it’s a job that he will accept,” Ogden said on ESPN FC.
“It’s a formality that he’s going to take the job and he couldn’t turn it down.
“But it’s a tough job to take on because Chelsea have lost their best player by a long way, Eden Hazard, they’re under a transfer embargo.
“It’s the right move for [Lampard], whether it’s the right move for Chelsea…
“Look, Chelsea’s ethos under [Roman] Abramovich has always been a churn of managers, they don’t stick around for very long.
“So if it doesn’t work for Frank Lampard it will only be the same as Maurizio Sarri going after a year or AVB going after six months or Scolari going after six months, it’s what Chelsea do.
“It will be quite painful to get rid of a legend but I think for Chelsea, why not?
“He’ll bring Jody Morris with him as a coach and Jody Morris was the coach of the young Chelsea team that won a lot of FA Youth Cups.
“So they will know the players coming through.
“So maybe this is the time where Chelsea become a team that gives their young talent a chance.
“But ultimately, I think Chelsea realise with the situation that they’re in, the transfer embargo, Hazard going, that the best coaches in Europe will say ‘well it’s not a good job to take right now’.
“So maybe Frank’s going to get it by default but it’s a great opportunity so why not?”