Wantaway Van Dijk 4-6 to seal Anfield switch from Saints
Brighton strengthen their midfield with PSV's Propper
Chelsea are 2-1 second favourites to sign the 26-year-old but he said earlier in the summer that Anfield is his preferred destination.
Van Dijk is 11-1 with Sky Bet to still be at Southamption after the summer transfer window.
Propper, who netted 16 goals in 66 games during his time with PSV, has arrived at the Amex Stadium for a reported club-record £6m and signed a four-year contract with the top-flight new boys.
McClaren is understood to be on the Tynecastle club’s shortlist to replace Ian Cathro, who was sacked after just seven months in charge a week ago.