Rangers have already snapped up Wes Foderingham, Danny Wilson and Rob Kiernan this summer, but new manager Mark Warburton is now turning his attention to other targets.
Sky Sports Transfer Centre (16:32) report that Rangers have made enquiries over moves to bring Wigan Athletic duo Tavernier and Waghorn to Ibrox this summer.
Tavernier, 23, came up through the youth system at Leeds United before joining Newcastle in 2008, but played just 11 first team games for the Magpies, spending most of his time out on loan before being sold to Wigan last summer.
After limited appearances for the Latics, Tavernier moved out on loan again, this time to Bristol City - though Wigan's relegation to League One could force him to move on this summer, with Rangers seemingly keen to add him to their squad.
Meanwhile, 25-year-old Waghorn emerged with Sunderland before a move to Leicester City, and the striker hit three goals in 24 games for Wigan last season before suffering relegation.
What would the duo offer to Rangers?
Tavernier is an attack minded full back with pace to make a difference in the final third, offering quality deliveries into the box - and with Rangers releasing Sebastien Faure and Richard Foster earlier this summer, a right back is certainly needed ahead of the new season.
Meanwhile, Waghorn is a hard working striker who can also play out wide, giving Warburton flexibility and versatility should he make the move to Glasgow this summer.
Both players have Championship experience, and would be vital additions for Warburton as he builds his squad ahead of the new summer.