Professional dancer Neil had missed the previous two weeks of the competition after sustaining a muscle injury, with Kevin stepping in to dance with Alex.
The paper quoted an unnamed source who said that Alex was “hopeful that she would be allowed some sort of consistency, and have Kevin on the night”, and complained the decision to reunite her with Neil was too last minute.
But the former England and Arsenal player denied the story, writing on Twitter: “Just woke up to this news…
“This is not the case at all ha. I think you can see from the joy on our face last night as we danced our jive.”
She added that “#teamred is very happy to back together.”
She told her followers: “Got to admit it though, I do feel like the luckiest girl alive.
“Not everyone gets to dance with two amazing people on Strictly. Who would ever want to complain about that, lol Kevin Clifton is part of #teamred.”
Neil added: “I started laughing when I read it this morning….
“Anyway who cares, we both had a great time and enjoyed every moment of that jive and that’s all that matters #teamred.”
The pair performed a Jive on Saturday night’s show, with Neil saying it felt “good to be back”.
However, he faced an awkward moment when judge Motsi Mabuse made a remark about an “affair”, with viewers immediately reminded of Neil’s now-estranged wife Katya kissing her celebrity partner, comedian Seann Walsh, on the street during last year’s series.
The couple announced their split earlier this year, suggesting their marriage had become more of a friendship than a romance.
Strictly Come Dancing continues on Sunday night at 7.15pm on BBC One.