Manager Angelo Alessio says Kilmarnock have no plans to sell Greg Taylor or fellow full-back Stephen O'Donnell this month.
Taylor, 21, has been linked with Celtic, and a £500,000 offer from Nurnberg was rejected in July.
O'Donnell, 27, is entering the final year of his contract and has reportedly rejected a new deal.
"I don't think either of these players can go to another team in this window," said Alessio.
"I want to keep the best players in our team, like Greg Taylor and Stephen O'Donnell. All I've read are rumours."
Rather than losing players, Alessio is confident of adding to the Kilmarnock squad, saying he is hopeful of making new signings on Monday.
"At the moment we're having some conversations," said the Italian. "It's difficult to bring in the right players because a lot of clubs and agents are offering players but we don't want to make a mistake.
"We need to bring in other players up front but this market is very difficult because other teams want the same player."
After a shock defeat by Connah's Quay Nomads in Europa League qualifying, Kilmarnock have lost their first two league matches.
The Ayrshire side, who finished third last season under now-Scotland manager Steve Clarke, host Hamilton Academical in the League Cup on Saturday looking to avenge last weekend's league loss in South Lanarkshire.
"I'm optimistic the first win will come soon because I see the team playing good football with fluency, creating plenty of chances," said Alessio. "But, at the same time, we're being punished for every defensive error at the moment.
"It's been tough but I'm enjoying the challenge. It's different; a different country; different football but I think it's important for me to give my team a good understanding of what I want to bring.
"We need to give more; we need to do better. We run a lot, we work hard on the pitch but at the end of the game we have no points."