The 33-year-old is currently without a club after his one-year contract with Preston expired at the end of the 2016-17 campaign, having featured just eight times.
The Denmark international was linked with Burnley earlier in the summer but they decided against sending an offer in Lindegaard’s direction.
However, Burnley have confirmed number one Tom Heaton is set for at least four months on the sidelines after dislocating his shoulder and Dyche has admitted he wants to bring in more cover.
Dyche confirmed that he has invited the former Manchester United keeper to train with the squad this week as he ponders whether to hand him a deal.
"He’s come in to spend a few days with us and enjoy what we do and we’ll speak to him accordingly,” Dyche said.
"Ideally, like any manager, you want three and maybe a younger keeper under that as well."