Following a comprehensive 3-1 win over Newcastle United on Boxing Day, United have now taken 22 points from their last eight top-flight outings and sit third in the table.
The form being shown by Louis van Gaal's team is fast making a nightmare 2013-14 campaign under the stewardship of David Moyes a distant memory, and has even led to suggestions that they could challenge Chelsea and Manchester City for the title.
Indeed, despite the fact they remain some 10 points adrift of Premier League leaders Chelsea, Carrick feels United are capable of upsetting the odds.
However, the in-form playmaker knows Sunday's trip to Tottenham - who he left to join United in 2006 - will provide his side's title-winning credentials with a stern examination.
"The signs have been good in recent weeks," Carrick told United's official website.
"We were bitterly disappointed not to win last week [United drew 1-1 at Aston Villa] but we beat Newcastle and now have two big away games [at Tottenham and Stoke]. They will be a good test for us to see where we are at.
"We're continuing to look up and will continue to try to catch them [City and Chelsea].
"We're not satisfied with third - it's obviously an improvement and we're getting better, but we want to keep looking up.
"Going to Tottenham is always a tough game and to go there two days after the Newcastle match at 12 noon makes it very tough.
"But we have to get ourselves ready for that and it's the same for them as well. It's a game we look forward to and we go there confident."
Tottenham will also approach Sunday's clash in high spirits after they recorded a third straight Premier League victory with a 2-1 win at Leicester City on Boxing Day.
That result moved Mauricio Pochettino's team to within two points of a place in the top four and, in Harry Kane, Spurs have one of the top flight's in-form forwards.
Kane opened the scoring with his fourth goal in as many games in the very first minute at the King Power Stadium on Friday, and has seemingly overtaken Emmanuel Adebayor and Roberto Soldado in Pochettino's striking pecking order.
Pochettino will be relieved to have goalkeeper - and, in the absence of the out-of-favour Younes Kaboul, stand-in captain - Hugo Lloris available, with the Frenchman fit despite a heavy collision with Jamie Vardy on Friday.
It is unclear whether Van Gaal will be able to call on Angel di Maria at White Hart Lane, though, after the Argentina star missed the win over Newcastle with a knock.
Belgian duo Marouane Fellaini and Adnan Januzaj are definitely out due to illness, while Daley Blind (knee) and Marcos Rojo (thigh) also remain sidelined.
Chris Smalling (muscle), Luke Shaw (ankle) and Ander Herrera (knock) could feature.
