The trio - who are among more than a dozen Fir Park players who are out of contract in the summer - are named on PFA Scotland’s list of players who are looking for new clubs.
Former Inverness and Ross County midfielder Vigurs, 27, has not played under Ian Baraclough after being sidelined by a back injury on the day the manager was appointed in December.
Carswell has only made two substitute appearances since Baraclough strengthened his squad in January but the 21-year-old midfielder has played a total of 98 first-team games for the club.
Versatile defender Ramsden, 33, made an impressive return to the team in Motherwell’s 3-1 win over Kilmarnock last Friday night after dropping out through suspension six weeks earlier.
Other Fir Park players whose contracts are due to expire this summer include Zaine Francis-Angol, Paul Lawson, John Sutton, Josh Law, Scott McDonald, Adam Cummins and Fraser Kerr while Lee Erwin is in advanced talks over a new deal.