have a thing going (with someone)
To have or be in the midst of a romantic or sexual relationship with someone. I hear you have a thing going with Jeff from accounting. Is that true? I have a thing going with a lady across town, but it's nothing too serious.
have a thing going (with someone)
and have something going (with someone)Fig. to have a romance or a love affair with someone. John and Mary have a thing going. Bill has something going with Ann.