The Baggies are after some reinforcements for the second half of the season as they sit 12th on the Premier League table, nine points clear of the drop zone.
Pulls is set to meet with Peace on Friday to discuss transfer matters an although the Welshman would love some new additions, he is not expecting the Albion chief to invest too heavily.
"I'm having dinner with Jeremy on Friday and we can sit down and have a quick chat about the way he sees it, the way I see it, and then we can go from there," Pulis told the Express & Star.
"Things are bubbling behind the scenes but nothing's come to the surface. Jeremy will decide.
"I had my views in the summer, Jeremy has got his views. The chairman runs the football club when it comes to the finances and it's his decision in the end what to do with it.
"He has run the football club in a very astute manner over the past 10 years. The football club has got a fantastic structure in place, it's debt-free, they make money most years. You have to give him enormous amounts of credit for that."
The Baggies are being linked with the likes of Tottenham winger Andros TownsendArsenal right-back Mathieu Debuchy (which has since been denied) while striker Saido Berahino's future at The Hawthorns is still very much in doubt.
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