A report in The Sun on Wednesday claimed that Barca have turned their attention to the Portugal international after admitting defeat in their pursuit of Arsenal's Hector Bellerin, while Juventus are also said to have shown an interest.
Southampton have already fended off an approach from Liverpool for defender Virgil van Dijk this summer, and Reed is confident that the club can keep hold of their big hitters ahead of the 2017-18 campaign.
"None of those players are for sale. I can't make it any plainer than that and that's the way we mean to go forward," he told Sky Sports News. "We built this squad over some time and think we have a strong squad. We will fine-tune it but, other than that, we are looking forward to a very competitive season next year and we plan to go forward on that basis.
"There may be players that go on the basis it is the right thing for them and the club at that given time, but we don't expect that to be wholesale and this is simply doing sound business in the transfer window. We track players over years and when the new manager comes in like Mauricio [Pellegrino], we take him through that process.
"He'd done his homework on our squad and we don't believe we need to turn over players every year just to freshen things up. We've got a strong squad now and it would be about adding players bringing more value and power. It's not broken so there is no need to bring in players just because of fashion or to get people excited in the transfer market."
Liverpool were forced to drop their interest in Van Dijk earlier this summer due to an illegal approach, but fresh reports this week suggest that they could be about to return with a £50m offer.