Indeed, the duo would be realistically out of the north London side's reach in terms of both signing due to the financial demands of West Brom and Palace, the Tottenham board have conceded.
The Standard suggest the club remain intent on selling a number of players but have their eyes on several recruits. West Brom's Berahino, though, will reportedly be worth £20 million or more, while Crystal Palace are said to still be holding onto their valuation of in excess of £40m for Bolasie.
A matter of preference
The choice is an intriguing one but, should the Standard's report prove true, it then becomes a matter of preference for Daniel Levy and Mauricio Pochettino.
A new striker is a must for Spurs, while Berahino should also be able to play out wide. Bolasie, however, could provide enough pace and skill out wide to increase the service to Tottenham's current strikers.
That would mean relying solely on Harry Kane once again or even holding onto the faint hope that Emmanuel Adebayor or Roberto Soldado could thrive on improved service, although they are both reportedly for sale.