Juve were also linked with Pogba over the summer though Real Madrid's interest has appeared to be stronger and more continuous.
And According to Spanish outletel desmarque, Real Madrid chief Florentino Perez will try to get Pogba by offering Bale plus 100 million euros.
It's reported that Bale is seen as being worth around £75m, meaning the total deal is likely to be over £150m.
United were believed to be wanting that figure during the summer for Pogba, though manager Ole Gunnar Solskjaer was keen to keep the World Cup winner in his squad.
Indeed, the Norwegian has regularly sung the praises of the Old Trafford academy graduate since taking over as boss last December.
Just last month he said: "I don't listen to the president of Real Madrid [Perez]. But Paul is working hard here and he is totally committed to Manchester United.
"We have seen that while he's been injured. He has been working like crazy to get himself fit because he wants to play for us and he wants to help his team-mates.
"I am not worried now and I will never be worried in the future about Paul Pogba staying here.
"If it all kicks off against with Madrid in January then there will beno worries then either. If we have to live with the speculation again then we will handle it like we did in the summer.
"Paul is going nowhere. He is happy here when he's playing."
Also, Bale has secured a full-time spot in the Real Madrid starting team but has only managed to score two goals so far this season, adding to Zidane's frustrations.
Bale nearly departed Real Madrid for China over the summer but the move was blocked by club president Florentino Perez. However, now it appears Perez is more on board with the idea of a swap, if they can convince Ole Gunnar Solskjaer and United. Pogba's current contract with the club runs until 2021.
