The Ageas Bowl outfit need to win at Nottinghamshire to have any chance of avoiding the drop and must also rely on other results to go their way.
But after winning the toss and putting the home side in at Trent Bridge, Hampshire were unable to build on a promising start with the ball as Nottinghamshire were eventually bowled out for 340.
Hampshire then lost a wicket to the opening ball of their reply when bowler Ryan Stevenson – sent in to open to protect the batsmen – was dismissed by the England Ashes hero.
And first-team coach Dale Benkenstein knows Broad could put another nail in the Hampshire coffin if he can produce a similar spell that destroyed Australia this summer.
Benkenstein said: ‘They have got a very good attack and a quality bowler in Broady so we will have to bat well and try to get our points with the bat.
‘If you look at what we were aiming to do, we have got our full bonus points with the ball so that’s a real positive for us.
‘But as far as the game goes, putting a side in, you would like to bowl them out for under 300.
‘I think we had a chance to do that and I don’t think it was our best bowling performance.
‘It is the end of the season and I think we saw a bit of that from both teams.
‘A few poor shots got us back into the game, but overall Fidel (Edwards) kept picking up wickets and that enabled us to bowl them out.
‘With a more polished performance, we would have liked to have bowled them out for maybe 260.’
Edwards was the pick of the Hampshire attack as he grabbed six wickets for 88.
But Benkenstein felt the rest of the Hampshire bowlers were unable to stem the flow of runs at the other end.
He said: ‘I would say it probably wasn’t his best bowling performance.
‘To his credit, he sussed out the conditions early on.
‘He didn’t bowl that quick but pitched the ball up and there was a bit of movement early on.
‘That’s what he does. He has been phenomenal.
‘He has got the highest strike rate in the first division so he has been a real credit to us.
‘Around him, we need to be a bit more miserly with the runs and that’s probably where we gave Notts a few too many runs.’
Hampshire now need to dig deep with the bat to give themselves a chance of forcing a win.
But the South African believes there will be just as much motivation for the home side to chase a victory.
He said: ‘Ideally, we want to get 400. The one thing that may work in our favour is that they also need a win to come second.
‘There is a decent amount of prize money to play for and you want to finish as high as you can.
‘At the moment, it comes down to us getting as many bonus points as we can.
‘If we can get a lead, it gives us a natural way of winning the game.
‘But if it doesn’t, then it may be a case of chasing something on the last day.’