The British athlete has demanded that the football club remove her name from the stand in Bramhall Lane if Ched Evans is offered a new contract.
The Sheffield-born sportswoman said the move would "completely contradict" her beliefs and she would be forced to sever links with the club if the convicted rapist was re-signed.
She said in a statement: "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."
Since her statement the Olympic champion has been the victim of trolls on Twitter and was sent tweets which suggested she deserved to be raped.
A troll, using a fake account sent an offensive tweet, which has since been deleted, writing: "Jessica Ennis-Hill is a stupid c***. Saying she will remove her name if Ched Evens (sic) is signed. I hope he rapes her.'
After being criticised for the threat, the troll replied: "Freedom of speech mate… I'll say what I want when I want!"
Several other Twitter users came to the sportswoman's defence and condemned the trolls.
"At least Jessica-Ennis Hill is trending because a lot of good people are standing with her against rapists and bullies. Rock on, Jen."
Another wrote: "Good for you Jessica standing up for your principles and the trolls are just a bunch of cowards!!"
Commenting on the trolls a police spokesman said: "South Yorkshire Police can confirm they are investigating reports of abusive tweets. Officers are making efforts to contact the individual concerned, but have launched an investigation into the posts."
The heptathlete is the latest high-profile figure to warn she will cut ties with Sheffield United if Evans is re-signed after Sheffield United allowed the footballer to train with his former teammates.
Rape threats against @J_Ennis are sick and vile. This is totally out of order.
— Nick Clegg (@nick_clegg) November 14, 2014
TV presenter Charlie Webster announced that she was resigning as a Sheffield United patron because the club had failed to recognise the "extremity" of Evans' crime. Health expert Lindsay Graham and 60s pop star Dave Berry also resigned as patrons of the club with Mr Berry stating that he was taking "a moral stand" over Evans.
Sponsors DBL Logistics and John Holland Sales Ltd also threatened to end their deals with Sheffield United if the striker was given a contract. John Holland car sales said it "condemns rape and violence of any kind against women" and would terminate their contract with the club if he played for them again.
Local MP Paul Blomfield warned the club's stance "sends a disturbing message to young people and victims of sexual violence" while Deputy Prime Minister Nick Clegg - a Sheffield MP - has suggested that Evans should consider moving abroad to play football so he can play again, because his club in the UK should not take him back. He has also condemned the "sick and vile rape threats" made against Ennis-Hill.
Sheffield United said it had granted a request from the Professional Footballers Association for Evans to be allowed to join training, but no decision on whether to re-sign him had been taken.
Evans, 25, was released from prison last month after serving half of a five-year jail term and continues to protest his innocence, claiming the sex was consensual.
An appeal against Evans's conviction was rejected by three judges at the Court of Appeal in 2012. His case is due to be looked at by the Criminal Case Review Commission. After his release, Evans posted a video on his website protesting his innocence and vowing to clear his name.
More than 160,000 people have signed a petition urging the club not to take Evans back.
A spokeswoman for Mrs Ennis-Hill said she would not be making a statement in response to the threats on Twitter.