Coleman, who only took over at Sociedad in the summer, was asked about Bolton's supposed interest at Thursday's press conference, but the former Fulham coach side-stepped the question.
Coleman has had a mixed start to life in San Sebastian with Segunda Division Sociedad, who were relegated last season after 40 years in the top flight, winning four and losing three of their opening eight matches.
That has left the Basque giants in eighth spot in the standings ahead of Saturday's visit of Sporting to the Anoeta.
Coleman admits there is pressure, but insists it is nothing new to him.
"There's pressure at every club and every job, outside of football, in normal jobs, everybody has pressure," he said.
"For me in football, I ask the players always to express yourself, work hard, play good football and express yourself.
"We all know that in the background there is always one word - promotion. I don't need to say that to the players, they know. We don't talk about it in training, they know, it's obvious."