Reports suggest QPR are demanding in excess of £15million to part with the striker, who scored 18 goals Premier League goals for the relegated London outfit last season.
The player's asking price has scared off the likes of West Ham United and Newcastle United but latest reports, such as those in the Evening Standard, suggest that Spurs are ready to meet the Championship club’s valuation.
Speaking to talkSPORT's Alan Brazil Sports Breakfast show, Sheringham was quick to express his views on the matter.
Indeed, the recently appointed Stevenage manager believes the 26-year-old would be an excellent acquisition by his former club.
When asked if Austin would fit in at Tottenham, he said: “Most definitely.
“He is a fantastic finisher and a great player to have around. To score 18 goals last season in a struggling team shows he can score goals.
“I wouldn’t care what the going rate was at the moment, I would snap him up.”
Austin scored 18 goals in 35 appearances for a team that finished bottom of the Premier League pile last term, while he created a further 23 chances, assisting five goals.
This saw him contribute directly to an incredible 43% of QPR's total goal output, making him the English top-flight's most influential player for his respective club.