I think that it's extremely unlikely that we will sign a striker, with the exception of Dembele who is more of a player for the future. 
We have known since August 31st that we only have Kane as an out and out striker.  The club had three months to prepare a transfer, and to agree a transfer, in principle, before the start of January. And yet..nothing.  We've since had almost a month and yes..nothing.  Why expect that to change almost overnight?  I think that Levy & Pochettino decided in August when we didn't get Berahino that we would make do with only Kane, and so we've not pursued any alternatives.