England forward Kane has scored 14 times in 22 Premier League outings for Spurs this season but faces an extended period on the sidelines due to an ankle injury. He is not expected back before the beginning of March.
Additionally, they are temporarily without Son Heung-Min, who is away on Asian Cup duty with South Korea.
As such, there has been speculation that the White Hart Lane side, who remain at Wembley as their ground redevelopment has run overschedule, could move for 31-year-old Rossi, a free agent since leaving Genoa in the summer.
“There are many names that appear in every transfer window,” said Pochettino, who became the first Premier League manager in history not to make a single signing during the summer transfer window of 2018.
“I think he is another name to add on the list but it is only a rumour. We have not considered him.
“I don’t think it’s a possibility.”
New Jersey-born Rossi started his senior career with Manchester United in 2004 but truly rose to prominence during his time with Villarreal in La Liga. However, his development was stunted by a series of serious injuries, which effectively cost him three seasons.
Fiorentina signed him up and, during the 2013-14 campaign, reaped the rewards of his goalscoring instincts as he notched 16 times in 21 games, though a knee injury struck in January when he was the league’s top scorer.
During his time with the Serie A side, he tested positive for the banned substance dorzolamide and, though he strenuously denied any wrongdoing, was given a warning.
In a bid to regain his fitness, he has recently been training with Manchester United, who are now managed by his former team-mate at Old Trafford, Ole Gunnar Solskjaer.He has won 27 caps for Italy and has scored nine goals.