The Patriots hosted three offensive linemen on tryouts Wednesday, according to a league source.
Heyer, 28, has played in 61 career games with the Redskins and Raiders, making 35 starts. Last season, Heyer started twice at left guard for Oakland.
The 27-year old Richard played in 48 games (11 starts) in four seasons with the Colts, after being drafted in the seventh round in 2008.
Keith, also 27, started 20 games at right tackle for the Cardinals over the past two seasons, before landing on injured reserve both years.
The Patriots' roster stands at 89 players, one shy of the 90-man limit. The team has 16 offensive linemen under contract, but the status of injured guard Logan Mankins and veteran guard Brian Waters remains up in the air for organized team activities, which are underway this week.