Spurs are in need of firepower with Harry Kane ruled out until April with a hamstring injury.
And Giroud looks set to leave the Blues this month after starting just two Premier League games this season.
Waddle, who played for Spurs between 1985 and 1989, likes Giroud, despite his close ties to Arsenal, a club he represented for six years before leaving for Chelsea in January 2018.
He told the Racing Post: “Olivier Giroud seems to be one of the big-name stars being linked with Spurs and I’m sure there are a number of clubs looking at the French World Cup winner.
“I like Giroud. I know he misses a few but he scores them as well which tells me he knows where to find space in the box to accumulate chances.
“Indeed, he’s getting better with age.”
LIVE on talkSPORT
Check out all the LIVE commentaries coming up on talkSPORT, below…
- Crystal Palace vs Arsenal (Saturday, 12:30pm) – talkSPORT
- Brentford vs QPR (Saturday, 12:30pm) – talkSPORT 2
- Chelsea vs Burnley (Saturday, 3pm) – talkSPORT 2
- Tottenham vs Liverpool (Saturday, 5:30pm) – talkSPORT
- Cardiff vs Swansea (Sunday, 12pm) – talkSPORT 2
Giroud has been heavily linked with a January move to Inter Milan, with his agent understood to be discussing personal terms with the Serie A giants.
On Friday, Chelsea boss Frank Lampard hinted he would let the France striker leave even if the club fail to sign a replacement this month.
He said: “Nothing’s done yet. With Ollie the situation is, if it’s right for everybody, and first and foremost that’s us as the club, then we’ll look at whether he can leave the club.