South Yorkshire police are investigating rape threats sent to Olympic gold medallist Dame Jessica Ennis-Hill after she said she would request the removal of her name from a stand at Sheffield United if it offers a new contract to convicted rapist Ched Evans.

Ennis-Hill received the abuse on Twitter, with one tweet, sent from the handle @RickieLambert07 reading: “Jessica Ennis-Hill is a stupid cunt. Saying she will remove her name if Ched Evens [sic] is signed. I hope he rapes her.” Both the tweet and account were then deleted.

After the troll was called “scum” for his threat, he replied: “Freedom of speech mate … I’ll say what I want when I want!”.

Another Twitter user, going by the handle @CoreyOC21, sent a message to Ennis-Hill which read: “Hope Ched Evans gets you you little slut.”

A spokesman for South Yorkshire police said: “Officers are looking into the tweets.”

The feminist campaigner Jean Hatchet, who started a campaign signed by more than 160,000 people on change.org calling on the club to break all ties with the player, told the Guardian she has been receiving up 500 abusive tweets a minute from supporters of the disgraced footballer.

Sheffield-born Ennis-Hill, who had a stand at Bramall Lane named in her honour after the Blades fan’s heptathlon triumph at the London 2012 Games, said in a statement on Thursday: “I believe being a role model to young people is a huge honour and those in positions of influence in communities should respect the role they play in young people’s lives and set a good example. If Evans was to be re-signed by the club it would completely contradict these beliefs.”

On Friday, David Cameron said he understood why Ennis-Hill had called on Sheffield United not to offer a new football contract to Evans. Speaking on the margins of the G20 summit in Brisbane, the prime minister told reporters: “I quite understand why she’s said what she’s said and done what’s she done.”

A Downing Street spokeswoman added: “The prime minister had previously pointed out that football players should regard themselves as role models and was sure Sheffield United would consider carefully before making any decision.”

Ched Evans during his trial at which he was found guilty and sentenced to five years’ jail for rape. Photograph: Martin Rickett/PA

The move will put further pressure on Sheffield United to publicly state that they will not offer a new contract to Evans, who was told he could start training with the club again this week after a request from the Professional Footballers’ Association.

Three patrons of the Sheffield United Community Foundation, including the TV presenter Charlie Webster, have resigned over the decision to let Evans train. Sponsors have also threatened to cut ties with the club if a new deal is offered to the 25-year-old, who maintains his innocence.

Evans, a former Wales international, was released from prison last month after serving half of a five-year sentence for raping a 19-year-old woman in a hotel room in Rhyl, north Wales, in 2011. The footballer had admitted having sex with the woman after his friend and fellow footballer Clayton McDonald had done so, while two other friends attempted to film the event through a window. Both men denied rape and McDonald was cleared, but Evans was sentenced when the jury agreed with the prosecution that the woman, who cannot be named for legal reasons, was too drunk to consent to sex.

Other MPs have also entered the row. Paul Blomfield, the Labour MP for Sheffield Central and a United shareholder, said taking back “an unrepentant convicted rapist” would send “a disturbing message to young people and victims of sexual violence about how we view rape”.

Nick Clegg, the deputy prime minister, urged the club to rethink the decision to let Evans train, and Labour’s Yvette Cooper said it was “in danger of sending the wrong signal”.

Two shirt sponsors have threatened to pull out of deals with the club. DBL Logistics said on Wednesday that it would end its arrangement if Evans was re-signed, while John Holland Sales said it would examine its position if the player was given a new contract.