There are at least three ways in which Boo shows that he wants to interact with the Finch children.
First, he mysteriously leaves gifts for them in a tree knothole. For example, Scout and Jem find: gum, Indian head pennies, replicas of them carved out in soap, and many other items. This shows that Boo is kind and desires to befriend them.
Second, when there is a fire at Miss Maudie's house and the people are outside watching, Boo comes over and puts a blanket around Scout. Of course, Scout who is transfixed looking at the fire, does not notice, but it does show once again that Boo is reaching out in friendship.
Finally, at the end of the novel, Boo is really a guardian angel. He watches over Jem and Scout and protects them and even risks his own life as he fights off Bob Ewell.
Boo Radley demonstrates a desire to interact with the Finch children in several ways. By closely inspecting the text several clues can be seen. The knothole where the Finch kids find several presents is one of these clues. Although the Finch kids think this knothole is merely a hiding spot for a child, it is revealed that Boo is actually putting gifts there for them. Another clue is shown on the night when Jem loses his pants at the Radley place after being scared off by Nathan Radley. The next day Jem finds his torn pants mended waiting for him, presumably by Boo. Through these acts of kindness, Boo shows the kids he is not actually that scary or weird and just wants to be friends.