The new defender told how the prospect of potentially being part of a special season at Fratton Park was too good to turn down.
That’s after the 34-year-old became a free agent this summer, after spending three seasons with Reading.
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Morrison told he potentially had the opportunity to continue operating at that level, but the intensity of Pompey’s interest and the project Cowley is putting together proved a greater attraction.
He said: ‘There were a couple who were flirting.
‘I think though sometimes you get that feeling, that if someone really wants you then you should go and play for them.
‘I just think what is going on here is really exciting.
‘I’ve been involved in promotion teams and they are some of the best years you can have.
‘The two seasons I got promoted were just brilliant and I speak to 70 per cent of the players in those teams still.
‘It is a memory you create which is brilliant, whereas sometimes you play in a higher league and success can be finishing in mid-table.
‘Success here is getting promoted - and what a great feeling that is. It’s a special feeling.’
Morrison completed his arrival on Tuesday, in a move which quickly accelerated when the opening presented itself for Pompey.
The Blues pounced to bring in the former Sheffield Wednesday, Birmingham and Charlton man on a one-year deal, as he linked up with his new team-mates in the warm-up win over Barnet.
Morrison explained how Cowley conveyed a plan with the depth of planning which made an immediate impression on him.
And his assessment of the squad he is joining is it’s now well placed to launch a serious assault on reaching the Championship.
Morrison added: ‘There’s a lot of detail in what the boss is trying to do.
‘That continuity is important, too. Portsmouth were really strong last season at home.
‘I really like the idea of Colby Bishop and Joe Pigott. I think they will score goals.
‘It sometimes takes time tor establish what you want to do, because there are 23 other teams who want to get promoted or beat you on a Saturday.