Blues boss Antonio Conte is hoping to bring in a number of new faces before the closure of the transfer window at the end of the month and would like to boost the club's quota of home grown players at the same time.
Rose has now emerged as a target and reports claim Spurs could be willing to cash in following his controversial comments over the club's pay structure and lack of signings this summer.
The player later apologised for his outburst in the press and Spurs boss Mauricio Pochettino has also insisted there is no issue with him, but there could still be some tension.
The 27-year-old is still on the sidelines as he battles back from a long-term knee injury, but that is not stopping claims suggesting that Chelsea will launch a £50million bid after the two sides have met in the Premier League this weekend.
Manchester United have also been linked, but Jose Mourinho played down talk of a move, and Rose may not get his wish of returning north just yet.