I absolutely don't want to see him replace Sissoko without the man being given a real chance in a Spurs shirt. That Sissoko-Barkley swap stuff really put me off in that regard.
But the man is admittedly the sort of archetype that would fit our team - he's big and powerful yet very good with the ball in tight spaces and when spreading it over long distances. His decision-making still needs a lot of work, but if he's cheap, we might as well go for him as another option for that No.10 role. He's not likely to be cheap, exactly, but the thing about him is that his contract's up in the summer of 2018 - come this summer, he'll only have a year left on his deal, provided he doesn't sign a new one between now and then. Everton might ask for Sissoko-esque money, and they might get it if all the big boys (City, Chelsea, United et al) start bidding for him (which they might do given his homegrown status, provided he keeps his form up). But that's dependent on him continuing his run of form, which, as you've pointed out, isn't something he's known to be capable of.
For us, I could see a bid for Barkley happening under a very specific set of circumstances - he adapts to Koeman's drilled, defensive system, maintains a modicum of form (but not too much of it), refuses to sign a new contract and is largely ignored by the big boys come July/August 2017. I wouldn't mind him coming in then - not as a replacement for Sissoko, but as an addition to the side.