Reports suggest the Sports Direct owner has already rejected a second £250m bid from Staveley.
And Given believes the deal could be a landmark moment in the club's history, should it go through.
He told the Daily Star: “If they get the right investment, hopefully Rafa can strengthen in January – that will be hugely important.
“If they don't then they could be under a bit of pressure.
“Rafa has even quoted himself saying he wanted players in the summer but didn't get the money from Mike Ashley again.
“This takeover deal needs to happen in the next few weeks so he can get the right backing in January.
“I do believe they can get back up challenging for the Premier League and Champions League football.
“It's a great stadium, the fans are unreal and it's a big club."
Looking ahead to the game Simpson said: “We want to keep it going now.
“It's confidence and momentum, especially in this busy period in December.
“To get a point at West Ham and then two wins, it's been a good eight days for us."