The TV mogul told Derek, 25, the Girls Aloud singer needs to focus on her work and that she would be better off single, it has been claimed.
Simon, 50, made his feelings clear to Derek in a man-to-man chat over dinner at his London mansion recently.
A close friend of Derek's told the Mirror last night: "Derek said Simon was friendly enough, but just very firmly told him exactly what he thought.
"During the dinner Simon told Derek, 'It's nothing personal, I just don't think Cheryl should be spending so much time with you so soon after her marriage breakup'.
After the dinner Derek said to me: 'I just could not thaw him out. He is just so firm about where he stands'."
Simon became Cheryl's career mentor after he hand-picked the 27-year-old Geordie beauty to replace Sharon Osbourne as a judge on the fifth series of X Factor in 2008. He has also supported her following the break-up of her marriage to cheating soccer star Ashley Cole.
"Derek told me Cheryl respects Simon more than anyone else and she knows it is down to him that she is where she is today," claimed the friend.
"She thinks he is wise and emotionally intelligent, which is why Derek is so scared that Simon's opinion could hurt them in the long run.
"Simon told Derek he didn't want to be mean to him, but he just wanted to make sure he did everything in his power to safeguard her happiness and career." The dinner took place in London last month, after Cheryl was struck down with malaria after being bitten by a mosquito on a safari holiday with Derek.
When Derek was invited to dine at Simon's home, he thought it meant the X Factor boss was giving his blessing to his relationship with Cheryl.
But Derek's friend revealed: "Almost as soon as he arrived Simon made it very clear what his true feelings were.
"Instead of being happy for them, he told Derek he thinks right now Cheryl should be single. He noted that she would never have got malaria if she hadn't gone off to Tanzania with Derek.
"Simon thinks she needs a more stable routine. He also pointed out to Derek that Cheryl is reluctant to give up the name Cole - in his opinion this speaks volumes about where she is emotionally.
"He went on to warn Derek of encouraging Cheryl to jump into a rebound relationship and said Cheryl should be concentrating on her career because the next few choices she makes are critical. Simon knows Ashley held Cheryl back.
"What hurts Derek so much is that he knows he is It's nothing like Ashley and he's willing to do everything and more to support Cheryl."
Simon may have reservations about Derek's relationship with Cheryl, but the rest of their friends and family seem thrilled.
"Apart from Simon, everything else is golden right now for them," added the source.
"They are spending every minute of the day together at the moment and loving doing simple things like playing Rock Band and painting.
"They are just so happy. Cheryl has been getting to know his family over Skype and her mum Joan loves him. And unlike Simon, Amanda Holden thinks they are great with each other."
The couple recently had a night out with Britain's Got Talent judge Amanda at the Peninsula Hotel in Beverly Hills.
The source continued: "Amanda could see that Cheryl is calling the shots and is more content than ever before.
"Cheryl knows Simon is just looking out for her, but I think both she and Derek wish he would just realise they are very much in love and committed to building a life together."
nothing A spokesman for Simon Cowell told the Mirror last night: "Simon is very happy with anybody that will make Cheryl happy.
"Simon only cares about her health.
"He wouldn't dream of telling anyone what to do in their private relationships.
"He just wants her to be happy and healthy, and that's all that matters.
"There is absolutely no way Simon would be advising her and him about her private life. He was worried about her health and is very relieved she seems to be well again."
