Lawrence said the Pirates could be in the market to buy striker Dickson on a permanent basis from Charlton in January while the club are also hoping to extend Anderson's loan spell from Reading until the end of the season.
Both Dickson, who scored a double on his debut against Brentford on
Saturday, and Anderson are on initial three-month loan deals.
But Lawrence told the Bristol Evening Post: "Chris had been on our radar for a while and made a great impact on his first game.
"His loan goes until the middle of December and we don't usually loan people unless we have some interest in buying them. Sometimes it is purely a loan, although that's rare for us.
"I'd like to think we could keep Mikkel until the end of the season, at least. I would hope it would be in the interest of all parties for him to stay with us because if he goes back there, he's only likely to sit on the bench, at best."