The classic 1970s sitcom starred her father Richard Beckinsale as Lenny Godber, cellmate to Ronnie Barker's Norman Stanley Fletcher.
Porridge will return for a special episode, again written by Dick Clement and Ian La Frenais.
Set 40 years on, Kevin Bishop will play Fletcher's prison inmate grandson.
Nicknamed "Fletch" Fletcher, Nigel is behind bars for a series of cyber crimes.
Beckinsale said in an interview for Radio 5 live, Afternoon Edition:  "I don't think that's such a terrible idea. I think that's quite nice really.
"When it's beloved characters and a beloved project, it's quite nice to have an imaginary, 'what is their grandson doing?'"
But Beckinsale, whose new film is Love & Friendship - a romantic comedy based on Jane Austen's novel Lady Susan - has no desire to make a cameo in her father's old show.
"In Porridge? You've got to be joking. It's a boy's prison. I'm not that versatile. Tea lady?"
Her father died from cardiac arrest at the age of 31 in 1979.
He appeared in all three series of Porridge between 1974 and 1977 and finished making the film version a few weeks before his death.
Beckinsale, who starred in 2012's reboot of Total Recall, which originally starred Arnold Schwarzenegger, does not now believe remakes are a good idea, she says.
"I think it's a shame sometimes when they take something that is almost perfect or perfect and then remake it. That's a silly idea.
"They should remake things that aren't very good and have another go at it."
The new episode of Porridge will be broadcast this summer as part of a landmark sitcom season to celebrate the 60th anniversary of the start of Hancock's Half Hour on BBC TV.
It will include contemporary follow-ups to Are You Being Served?, Keeping Up Appearances and Up Pompeii! while lost episodes of Steptoe and Son, Till Death Do Us Part and Hancock's Half Hour will be remade from their original scripts for BBC Four.
The interview with Kate Beckinsale can be heard on Radio 5 live's Afternoon Edition on Tuesday 31 May at 1300.
Love & Friendship is currently in UK cinemas.

The 26-year old rejoined Stanley in the summer after spells at Stockport, Barrow and Chester on an initial one-year contract.
McConville has scored five goals in 28 games in his second spell at the club.
"Goals and assists are a plus but the most important thing is working hard for the shirt and I think I've done that," said McConville.
Stanley boss John Coleman said: "He won't be the last to sign up. We expect a few more to be putting pen to paper over the coming weeks."
Hollywood actress Kate Beckinsale, best known for the Underworld Series of films, has given her blessing to the BBC bringing back Porridge.
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Midfielder Sean McConville has signed a new deal with Accrington Stanley until the summer of 2018.