The New York Post said a source confirmed a deal was close but that details needed to be resolved.
House reported to Celtics practice Wednesday in Los Angeles but told The Boston Globe he expected to be a Knick by the time the trade deadline arrived at 3 p.m. Thursday.
"At the end of the day, this is a business, and the Celtics feel they will be a better team with the guys they are trying to get,'' House said.
It's widely assumed the Knicks do not intend to re-sign Robinson and would be moving him partly as a favor to their most popular player as well as to open up an opportunity for rookie Toney Douglas.
Robinson, 25, was scratched for the Knicks' home game against the Bulls Wednesday. According to The Globe, Celtics president of basketball operations Danny Ainge has long coveted the 5-foot-9 Robinson, who has claimed three slam-dunk titles at the NBA's All-Star weekend.
House, 31, is shooting 40 percent from the field and 38 percent from the 3-point line, both lows as a Celtic.