Warburton, 52, was appointed Rangers boss on Monday, signing a three-year deal to replace Stuart McCall in the Ibrox dugout.
The Englishman now needs to immediately begin to re-shape his thin squad, with 11 out-of-contract players leaving on free transfers this summer.
The Sun believe that Warburton already has his eye on his first signing, with Brentford winger Stuart Dallas on his radar having worked together previously.
Warburton left Brentford this summer after an immensely successful spell with the club, but could now lodge a £1.5m bid to reunite with Northern Ireland international Dallas - who wants the move to Glasgow, according to The Sun.
Dallas contributed eight goals in 44 games this past season for Brentford, whilst he even scored his first goal for the Northern Ireland national team last month, showing that he is a player heading in the right direction.
As well as snapping up the 24-year-old left winger, Warburton is also allegedly eyeing up a move for Brentford centre back Alfie Mawson, who is out of contract having snubbed a new contract to stay at Griffin Park.
Mawson, 21, impressed during a loan spell with Wycombe Wanderers this past season, but could now make the move up to Scotland to reunite with Warburton - if the new Rangers boss gets his wishes.