Boston declined the $5 million club option it held for Varitek, but the veteran has until Saturday to notify the team if he will exercise his $3 million player option.
If Varitek declines his option, he will be a free agent for the second consecutive offseason.
Once the Red Sox acquired Martinez in a trade with the Indians on July 31, Varitek suddenly found himself playing a reduced role after serving as Boston's primary catcher for the past decade.
In the 30-year-old Martinez, who also plays first base a couple of days per week to rest his legs, the Red Sox have one of the most potent bats in the American League.
"We're going to really look for Victor to be an everyday catcher for us next year," Red Sox general manager Theo Epstein told a group of Boston reporters at the General Managers' meetings in Chicago. "We feel like that puts us in the best position to win with Victor catching as much as he can. The other spot we'll have available is for more of a traditional backup. We'll see what Tek's decision is before we move forward."
To get Martinez from the Indians, the Red Sox put together a prospect-laden package that included swingman Justin Masterson and Minor League pitchers Nick Hagadone and Bryan Price.
In 56 games with the Red Sox after his arrival, Martinez hit .336 with eight home runs and 41 RBIs, finishing the season with a .303 average, 23 homers and 108 RBIs in 155 games between Cleveland and Boston.
"He really sees himself as a catcher," Epstein said. "We have to be smart about it. We can't push him to the point where we get diminishing returns. But I think he can catch a little bit more and he'll prepare himself to do that."
Once a solid contributor on offense, Varitek has been reeling at the plate for the better part of the past two seasons.
The 37-year-old Varitek started 106 games in 2009, hitting .209 with 14 homers and 51 RBIs. He has been the captain of the Red Sox since 2005.
In 13 seasons with Boston, Varitek has caught 1,381 games and ranks among the club's all-time leaders in games played (ninth, 1,439), doubles (eighth, 290), home runs (12th, 175), RBIs (15th, 705) and walks (15th, 583).
Would the Red Sox be comfortable using Varitek as a backup?
"I think so," Epstein said. "There's a school of thought that he'd be better with a little more rest."
During the regular-season finale of 2009, manager Terry Francona took Varitek out in the middle of an inning so that he could get a hearty round of applause from the Fenway Park faithful. It remains to be seen if that was a going-away cheer for the gritty catcher. The decision of whether to pursue more playing time elsewhere, return to Boston or perhaps retire is now in Varitek's hands.
In other business, the Red Sox reached a two-year, $10 million deal with veteran knuckleballer Tim Wakefield.
Ian Browne is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.