The 30-year-old joined Newcastle United on loan in January and has made nine appearances for the Magpies in all competitions, including seven in the Premier League.
Steve Bruce's side are thought to be keen on a permanent deal for the left-back, whose contract at the Tottenham Hotspur Stadium is due to expire next summer.
However, according to Corriere dello Sport, Lazio are also considering a move for the experienced defender as they look to boost their squad for the 2020-21 campaign.
Simone Inzaghi's side are currently battling Juventus at the top of Serie A, while the White and Sky Blues are 20 points clear of fifth-placed Roma, meaning that they are in a very strong position to secure Champions League football for next season.
Rose has made over 200 appearances for Tottenham over the last 10 seasons. body check tags ::