Johnson has emerged as Brentford’s top target this summer and they failed with an offer for him earlier in the transfer window.
But the Bees refused to give up on the prospect of signing the winger and continued to work on returning with an improved bid.
And it has been claimed that Brentford tabled a bid worth £40m to secure a deal to sign the winger from Forest.
The offer included a guaranteed fee of £35m and the rest was built on add-ons to reach the final figure.
However, Nottingham Forest wasted little time in rejecting the bid and have taken a hardline stance on Johnson this summer.
Forest do not want to sell their homegrown star but their resolve could be tested if they receive a bid in the region of £50m this summer.
It remains to be seen whether Brentford come back with a third offer to put more pressure on the Midlands club.
