The Sun says Spurs are locked in a £7million race with Lyon to sign Lovren.
Harry Redknapp is keen on the Croatia defender and has been in contact with Dinamo.
Lovren, 20, can also slot in as a defensive midfielder.
But Spurs have so far refused to enter a bidding war with Lyon - who have offered around £7.5m.
A top Dinamo source said: "Redknapp is very interested and has sought information on Dejan.
"Lyon have made an offer but Dinamo are looking for more money."