And the midfielder has backed the Blues to overcome Ipswich next Tuesday to secure the date.
Last night’s FA Cup fourth round draw saw the winners between Pompey and Mick McCarthy’s side presented with a home tie.
There they will face the Cherries, who have taken encouragingly to the Premier League this season.
The Tractor Boys forced a Tuesday, January 19 replay following a late leveller in Saturday’s third round clash.
The result was harsh on Paul Cook’s side, who produced one of their finest displays of the season in the 2-2 Portman Road draw.
Now a fixture with Eddie Howe’s side awaits.
However, before then the teams must be separated.
Evans said: ‘It’s going to be a tough one if we get through what is already a tough tie in Ipswich.
‘It’s also exciting to think we could be playing against a newly-promoted Premier League side who have actually not really shown signs of being a newly-promoted side having beaten Manchester United and Chelsea.
‘I don’t think they will be particularly thrilled about coming to Fratton Park. I can’t see them fancying coming down – and if we give everything we have got it could be interesting.
‘They are not far away from us which probably ups the game and the rivalry a bit more and it is definitely one to look forward to.
‘But we’ve just got to put our minds to Ipswich first, which makes it difficult to focus too much on the next round.
‘We know how good Ipswich are, as a club and as a team.
‘They are in the top six of the Championship so we are fully aware it is going to be a really tough game – but we fancy ourselves to give them a game again.
‘If we win then we have a Premier League team at home in the next round. There’s definitely a bit of a carrot dangling there.
‘It’s just unfortunate we didn’t end up going through first time, but if we play like that on Tuesday I am sure we’ll meet Bournemouth.’
Pompey were one of the final teams drawn out for the fourth round, with fixtures to be played between January 29 and February 1.
And Evans, who was watching the televised draw sat in his Winchester home, was dreaming of one particular team remaining in the proverbial hat.
He added: ‘I thought we were going to get Chelsea at one stage!
‘There were only seven teams left in it once they pulled us out, so I was hoping they would be next.
‘As it was, it’s Bournemouth and a good tie. It’s one to look forward to if we can get through next Tuesday against Ipswich.
‘We’ve got potentially a Premier League side – and I’m happy with that.’