Manchester United are heavy favourites to sign Rose, with The Express reporting Rose is keen on a move to Old Trafford.
Tottenham do not appear too concerned, with Rose dropped for the last two Premier League fixtures and not even on the bench.
Sessegnon is more Gareth Bale than Danny Rose, scoring a hat-trick for the Championship side last week, and is just 17.
But Manchester United could seriously throw Tottenham's transfer plans into a tailspin by moving for Sessegnon themselves.
A Manchester United move for Sessegnon would leave Spurs in a difficult position.
Mauricio Pochettino would either have to make amends with Danny Rose, or perhaps even do a deal with Chelsea, which they would be reluctant to do.
SkySports report that Tottenham's second choice left-back signing would be United's Luke Shaw, who could be used in a player plus cash swap with Rose, but Spurs would be in a significantly weaker position if the Red Devils have no need for Rose.
United's interest in the player makes it essential that Tottenham make their move for Sessegnon, and they should even consider signing him before cashing in on Rose.