The pair, who have been in a relationship with each other in the past, are said to have gone on a secret dinner date earlier this week and spent the rest of the night "all over each other" at a club.
Wright "playfully lifted her skirt" and made a "huge fuss" of Faiers as they spent the night flirting at the launch party of the new series of The Only Way Is Essex, according to The Sun.
Wight told the paper: "Sam's a great girl. I'm single these days so I'm just having a bit of fun. All I'll say is, 'Never say never'."
Faiers added: "We just get on so well. And of course he's really good looking. I'm not getting into anything serious."
The reality stars are said to be concerned that Wright's ex-fiancée Lauren Goodger will be furious if their relationship becomes more serious.
Faiers has previously insisted that Wright loves her. He split from Goodger last month.