The singer revealed that she hasn't been in contact with her former X Factor mentor for more than a year and so was surprised to receive a tweet from her recently.
"I haven't heard anything from Cheryl for over a year and then she tweeted me publicly the other day, which I was really surprised about," Burke told the Daily Star Sunday. "I've texted her a few times but never heard anything back.
"I was surprised to hear from her on Twitter, which was very public. Don't get me wrong, it was great for her to get in touch and it was a very lovely message, but I would prefer to hear from her more privately and maybe go for a drink and catch up properly.
"We kept in contact after the show but then it just stopped. You just don't know what is going on in other people's lives so you can't get mad if someone doesn't text you back. But of course it doesn't mean that I don't miss her. I miss her very much."
Burke added that she is still in touch with Beyoncé after they famously dueted during the 2008 X Factor final.
The 'Elephant' star, who landed at number two on the midweek chart on Wednesday, recently confessed that people assume she's a "bitch" before getting to know her.
Burke described Cole as 'more than a mentor' back in 2009, when the pair were said to be planning a duet.
Watch Alexandra Burke discuss a possible David Guetta collaboration below: