Jason Wilcox, the director of football at Southampton, acknowledged that Chelsea is now in the lead despite Liverpool having had a bid for Romeo Lavia accepted.
Three offers, totaling £45 million, were previously turned down by the Reds for the 19-year-old midfielder.
Jordan Henderson and Fabinho, who left for the Saudi Arabian teams Al-Ittihad and Al-Ettihad, respectively, leave a void for Jurgen Klopp's team to fill.
Liverpool attempted to acquire Moises Caicedo from Brighton for £110 million, but Chelsea beat Liverpool to the deal by making a $5 million higher offer.
Despite the Reds eventually paying Southampton's asking price, the Stamford Bridge club is now close to signing Lavia.
"I think you know, it's well known that we've had some significant interest in Romeo, we've had an offer that we accepted from Liverpool," Wilcox stated at the BBC Radio Solent Fans' Forum.
Chelsea then arrived to the table. As a result, Romeo is having a really difficult time right now because we're now negotiating with Chelsea.
But I'm optimistic that something will be accomplished in the coming week or few days.