The Gers pair impressed last season under Steven Gerrard. Brighton have become the latest side to have shown interest in Tavernier.
Kamara joined the Ibrox club during the January transfer window, but Brighton boss Graham Potter wants to sign both of them.
However, Rangers have no intentions of selling them at the moment.
The interest in Tavernier does not come as a big surprise.
The 27-year-old defender has enjoyed a phenomenal 2018-19 season, scoring 17 goals and providing 20 assists in all competitions.
According to recent reports from Football Insider, Aston Villa are also looking to lure him away from Ibrox this summer as Dean Smith is keen to add a solid right-back to his ranks.
Villa could make a formal approach for him following their promotion to the Premier League, but it seems they have competition here for Tavernier’s signing.
Ideally, Rangers would love to keep hold of their club skipper. However, if Tavernier wishes to join any Premier League side, the Gers should demand a high transfer fee for him.