The pair have been told they are not in contention for first-team football at their respective clubs, and Spurs are one of a number of teams interested in both players.
Sky Sports understands that Song, 26, who spent seven years at Tottenham’s arch rivals Arsenal, is keen to move back to the Premier League despite interest from Napoli and Galatasaray, and Spurs' only serious competition at this stage is from London rivals West Ham.
Welbeck, meanwhile, is also wanted by Newcastle, Sunderland and Hull City but is believed to be keen on a move to White Hart Lane.
Spurs boss Mauricio Pochettino watched the 23-year-old England international feature in Manchester United’s humiliating Capital One Cup defeat to MK Dons on Tuesday night and is yet to move formally for the forward.
Spurs remain active in the transfer market and are keen to strengthen their midfield after difficulties over a deal for Southampton’s France international Morgan Schneiderlin.
Sky sources understand Spurs still hold hope of resurrecting a deal for Schneiderlin, but may decide Song is a better proposition this summer.
Southampton have staunchly resisted Tottenham's advances for Schneiderlin, whilst approaching Spurs about Andros Townsend's availablity, only to be knocked back.