The Saints are yet to bring in any new faces during the January transfer window, despite selling Virgil van Dijk to Liverpool for £75m at the very beginning of the month.
Southampton have sunk into the relegation zone in the meantime following a run of 11 league games without a win, but Pellegrino is expecting more promising news in the coming days.
"Hopefully next week will be a good week for us," he told reporters at his post-match press conference.
"But in the market everything can change in one second. It is football. Negotiation is about two sides."