McLeish had a £20million war chest in January, but spent only £6million of that.
But the Scot fears the £20.5million loss suffered during the final year of the club’s previous owners could affect his plans.
McLeish said: “Nobody has said last season’s losses would affect things. We were talking about spending £20million in January and I only spent £6million of that.
“I would imagine that remaining £14million, plus whatever there is available to be spent this summer, means we should be reasonably healthy.
“But, if we want to remain a Premier League team and certainly get to where we are now, season after season, then you have got to keep up with the Joneses.
“Do I have to spend quite a bit to keep up with them? Yes, we need to improve again and enhance the squad.”
McLeish added: “In forward areas we need to add to the quality – and these areas are not cheap. You don’t get cheap players coming in there.
“We have spent, I think overall, during the season, about £15million or £16million. But that was for about six or seven players.
“To get six or seven players for £16million this summer, I think will be well-nigh impossible, unless we can get four or five Bosmans.”