The 22-year old has been linked with a Hawthorns exit all summer but doubts were cast over his move after West Brom placed a £25 million valuation on him.
The report claims a deal will likely be struck at around £20 million however, with Spurs opening proceedings with a £15 million bid.
Spurs are also set to announce the signing of Clinton N’Jie imminently, after he underwent a medical on Friday - as per the Telegraph - but additional attacking reinforcements are expected.
N’Jie is viewed as an option for either flank and an emergency back-up for Kane rather than a like-for-like alternative.
Berahino on the other hand, would represent the quality centre-forward Spurs fans have been crying out for to lessen the load on their academy graduate.