Ranson has promised to back Coleman in the transfer market as the Welshman attempts to build a squad capable of challenging for promotion to the Premier League.
But Coleman is determined to spend the cash wisely and not risk compromising the club's long-term future.
"It's the easiest thing in the world to sign a cheque for £2million but you have to make sure you get it right because in our league it can be disastrous if you don't," Coleman told the Coventry Telegraph. "As a manager you have to understand the business side of things because you have got to be careful because it is scary to see what has happened to other clubs.
"Look at Charlton, Southampton and Norwich - if it can happen to them it can happen to anyone. Going slowly is better than gambling.
"If you gamble and it comes off - great. But if it doesn't come off then the consequences can be massive. As I said on day one, I signed a long contract because I knew it would take a long time to get players out and my own players in."