New Spurs boss Mauricio Pochettino appears determined to kick-start the club's summer spending by making a move for Lovren, who he signed from Lyon at Southampton last summer.
Liverpool have already had a £12 million offer for the Croatian centre-back rejected, but Lovren has tried to force a move away from Southampton by handing in a transfer request.
Lovren enjoyed a successful first season in the Premier League, and has attracted the interests of big clubs across Europe, including Barcelona.
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The defender is currently in Brazil with Croatia, but Spurs will reportedly meet with Lovren's agent next week to discuss details of a potential contract.
The North London club are also thought to be tracking Adam Lallana - another Southampton player who thrived under the Argentine manager last season.
Tottenham also need to bolster their defence as the futures of both Younes Kaboul and Michael Dawson remain unclear, whilst Jan Vertonghen has been linked with a move away from North London.