Everton sacked Ronald Koeman in October and turned to former England manager Sam Allardyce, who has made them more hard to beat, but the Merseyside club have not won in their last four Premier League games and they were dumped out of the FA Cup by neighbours Liverpool a week ago.
Tottenham have moved to secure Dele Alli's long-term future.
With no imminent arrivals for Tottenham, Mauricio Pochettino admits the club's transfer activity is now frozen.
His current deal is set to expire in 2019, however, in that contract is a release clause, which becomes active when Tottenham trigger the option to extend the deal by an additional year.
However, Pochettino is not bothered by either the club's January inactivity or other rivals' spending after Liverpool signed Virgil van Dijk for £75m.
Nevertheless, Allardyce did manage to hold Chelsea to a 0-0 draw before Christmas and has seen his team push Manchester United (2-0) and Liverpool (2-1) close this month in the league and FA Cup respectively. He was on loan from Atletico Madrid with Spurs eventually signing him on a permanent. They need a long-term replacement for Ronaldo's goals, while Karim Benzema has only weighed in with two league goals this season, and their recent lack of big-spending is comparable to a smoking volcano waiting to erupt.
Son then played in Dele Alli, who failed to find the finish as he shot into the side netting, before Pickford was forced into action once more by a fierce low drive from Kane.
Spurs may well be able to persuade Kane that he can achieve all of his ambitions with them, but even the man himself has spoken recently of the need for the club to win trophies now.