Bosses reckon the rugby hunk - who split from Charlotte Church, 24, in May - will help 'sex up' the BBC show.
'I can't lie, I really like Strictly,' Gavin, 28, has said in the past.
Politician Ann Widdecombe, 62, and actress Felicity Kendal have also been approached.
Meanwhile, Bruce Forsyth is reportedly planning to cut back on his presenting duties on Strictly this year because he finds the schedule 'too exhausting'.
The 82-year-old is expected to stop hosting the Sunday results show.
The new series of Strictly Come Dancing kicks off in September.
- Lose weight with Strictly Come Dancing
- Gavin Henson and Charlotte Church split
- Charlotte Church flees the country