Ben, from Sheffield, South Yorkshire, was 21 months old when he disappeared on the Greek island on 24 July 1991.
Speaking on ITV's Good Morning Britain, Kerry Needham said she had been warned to "prepare for the worst".
Police searches have entered a third week after it emerged he may have been accidentally killed by a digger driver.
Mrs Needham said: "I think it really now is a case of finding him not alive.
"We can't live another 25 years like this, my parents can't and I can't.
"It's not the best solution but it will eventually lay it to rest for us, we're all extremely tired and distressed."
She added: "Twenty-five years living and not knowing where your child is is torment.
"I don't like to say it, but then at least we would know and it would be closure and he can be laid to rest and we can remember him as he was."
Mrs Needham said it was an "agonising wait every day" for news from the police.
She said: "Unfortunately it looks like it's going to be a bad outcome but we'll just try to get on with everything."
About 60 items found in the search are being sent back to the UK for analysis, with police extending their stay to search a second site 750m away from where he was last seen.

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."
The mother of missing toddler Ben Needham has said she now believes her son is likely to be found dead after disappearing on Kos 25 years ago.
[NEXT_CONCEPT]
Hollywood actress Kate Beckinsale, best known for the Underworld Series of films, has given her blessing to the BBC bringing back Porridge.
[NEXT_CONCEPT]
Midfielder Sean McConville has signed a new deal with Accrington Stanley until the summer of 2018.