The Sheffield Wednesday midfielder is on loan at Gillingham until the new year.
Clare has impressed for the League One side, scoring one goal and creating another in 14 outings, but his temporary deal is due to expire on New Year's eve.
And Lovell, who coached the 21-year-old at Charlton Athletic, hopes that Wednesday will extend his stay at Priestfield.
"Sean is having a good run with us and doing well," said the 57-year-old, as quoted by Kent Online. "If Sheffield Wednesday are OK with (extending the deal) then great.
"We are pleased to have him here. He is enjoying his football and he’s a good lad, very professional and a good athlete.
"He can run, he can move, he can read the game well and has great feet. He showed that on Saturday (against Bury) and was one of our better players, consistently, in the 90 minutes.
"Sean is one of the first names down on the team sheet every week and if he keeps playing like he is doing, then that will continue to be the case."
Midfielder Clare - who has filled in at right-back in recent weeks - was signed by previous Gills manager Ady Pennock in August, and their next boss's identity may have a bearing on his future at the club.
The former Nike Academy talent has also enjoyed temporary spells at Accrington Stanley and Bury, but is still awaiting his first appearance for Wednesday, for whom he signed in early 2016.
Clare is highly regarded at Hillsborough, nevertheless, and signed a new one-year contract ahead of his move to Gillingham.
Should Sheffield Wednesday sanction a longer stay for Clare at Gillingham?