"We are studying the market," Pellegrino, who replaced Claude Puel as manager at St Mary's in June, told reporters.
"We have got some options and always we can improve the squad. We will keep going and after we will wait to see what happens.
"The market is difficult, a lot of important teams are challenging for the best players. We are confident that someone can come."
Southampton are also tackling the uncertainty around defender Virgil van Dijk's future after he was left out of training last month.
Pellegrino said he expects to see a "different dynamic" from his team when they host Sevilla in their final pre-season friendly match on Saturday.
Following a 3-0 victory over St Etienne last weekend, the Argentine was disappointed to see an underwhelming performance when they were beaten 4-0 by FC Augsburg at St Mary's on Wednesday.
"Hopefully we can change the face in the next game, because we don't have too much time, but I think for sure we cannot repeat the same situation on the pitch that we had (against Augsburg)," he added.
Pellegrino's side kick off their league season against Swansea City at home on Aug. 12.
(Reporting by Hardik Vyas in Bengaluru; Editing by Robin Pomeroy)
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