SIRTE, Libya, June 1 (Reuters) - A deal to solve the case of five Bulgarian nurses and a Palestinian doctor sentenced to death for deliberately infecting Libyan children with HIV may be close, a spokesman for the children's families said on Friday. "We might reach an agreement on the Bulgarian nurses and the infected children before June 21," Driss Lagha, chairman of the Association for the Families of the HIV-infected Children, told Reuters.