And he is adamant the club are doing everything possible to recruit the right calibre of player.
Pompey remain firmly in the hunt for Preston’s Eoin Doyle ahead of Tuesday evening’s January transfer window deadline.
However, any prospective loan deal is likely to take place after the weekend.
The striker is expected to be involved in North End’s game with Ipswich tomorrow’s following a knee injury to Jordan Hugill.
But Lilywhites boss Simon Grayson remains open to loaning out the 28-year-old for the rest of the campaign.
The Blues’ ongoing pursuit of the ex-Chesterfield player is being threatened by fierce competition from Bolton and several other clubs.
Cook has declined to discuss his interest in Doyle.
Although Pompey’s manager moved to assure supporters of his determination to add quality to his promotion-chasing squad before the transfer deadline.
He said: ‘I won’t answer a question on Eoin Doyle because he would be on a list of how many? A lot.
‘If possible, we want to recruit something better than what we’ve got.
‘Every signing is a different sort of signing.
‘If you look at Jamal (Lowe) and Nicke (Kabamba) coming in, they are what we call progressive signings.
‘But I think the fans want the one that everyone goes “Yes” – and we are doing our best to give them what they want.
‘There is so much involved in any deal, you have to be respectful of it. Everybody out there at all clubs is looking for certain types, you only have to see the different signings people around us are making.
‘We are actively doing our best, and I can assure the fans we are getting all the backing in the world.
‘So you won’t see me Wednesday sulking about lack of signings if nothing could be done. Not at all.’
Preston remain interested in snapping up free-agent Robbie Keane before Tuesday’s deadline. In the meantime, they are unwilling to let Doyle depart until a replacement has been finalised.
The fact they face Cardiff City on Tuesday – the same evening as the transfer window shuts – means Doyle’s destination is likely to be decided on Monday.
For the Blues, the wait continues.
Cook added: ‘If we had to go with the same squad, I do believe we can get to where we want to be.
‘But we are actively looking to strengthen and bring someone in. The club have made enquiries in a correct and proper manner.
‘If it is something we can do I am sure our supporters would be happy.
‘If it’s not then there would be no blame attached to anyone. We will have done our best.’