The former Chelsea and England midfielder has still not featured for the MLS club through eight games of the campaign after suffering a calf strain during preseason.
Rangers will seek further squad improvements this summer.
Leicester City are closing in on the Premier League title.
The Blackburn boss announced on Thursday that he is to leave Ewood Park at the end of the season, but is still expecting his players to remain professional.
The Rossoneri are out of sorts in Serie A but could be rejuvenated with the signing of this England international.
The French winger found himself in a Twitter spat with ex-Aston Villa defender Shaun Teale.
The Cherries are currently 10 points above the bottom three.
The 19-year-old centre-back made his first-team debut for the club in last Saturday's 4-2 defeat to Southampton.
Townsend has scored three times since his January transfer.
Tottenham Hotspur boss Mauricio Pochettino has verbally agreed a new contract which will keep him at White Hart Lane until 2021.