However, he added the brothers might not be ‘everyone’s cup of tea’.
Coleman made the remark as the Blues prepare to host Accy at Fratton Park on Saturday.
Pompey go into the game hoping to extend their current unbeaten run to six matches, while the visitors travel hoping to avoid a fifth successive away defeat in the league.
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The Blues’ current form has seen them move to within eight points of the play-offs while having two games in hand on sixth-placed Sunderland.
And while Coleman admires Danny and Nicky for what they have already achieved in the game and their vision for Pompey, he acknowledged their approach might not go down so well among other managers.
He told the Accrington website before Saturday’s game: ‘They (Pompey) are a good side so it will be difficult.
‘I have a lot of time for the Cowleys, they have been different for football, their approach is different, probably not everyone's cup of tea the way they go about themselves, but I just love people who are so dedicated to football and improving football and improving themselves.
‘I have a lot of admiration for Danny and Nicky for the way they conduct themselves.
‘They love football and are not afraid to show it, they try new things and keep learning and have done well at the clubs they have been at.
‘They have a chance to take a really big club wherever they want.’
On Accrington’s last visit to Pompey - on the final day of the 2020-21 season – they beat the Blues 1-0 to deny Cowley & Co a place in the play-offs.
In October, the two sides drew 2-2 at the Wham Stadium, with Coleman calling the Blues’ support that day ‘a breath of fresh air’.