Linfield midfielder Kyle McClean said "there is no talks of leagues" and "absolutely no pressure on us at the minute" after the Blues' 1-0 victory over Glentoran.
After Tuesday night's big win over Dungannon Swifts, David Healy said that retaining the Gibson Cup was "unlikely, but not impossible".
However, after Larne's defeat on Friday and Linfield's derby win over the Glens, the odds are now more in their favour than they were a week ago.
Despite a shock Irish Cup exit at the hands of Championship front runners Limavady United, the Blues are now nine games unbeaten in the league and are hitting form at the sharp end of the season, aided by Matthew Fitzpatrick's goalscoring run.
"From the turn of the year, we know we have been in good form in the league and we knew we were on a good run," McClean told BBC Sport NI.
"We knew that we needed to be better from the first half of the season and we are taking it game by game. There is absolutely no pressure on us at the minute.
"We are just going about our business and trying to win games and trying to get up the table.
"Thankfully in recent weeks we have done that and certainly in that dressing room we are just wanting to win game by game and see where we end up in the league."
Linfield may be playing things down, but Healy's reaction at full-time, where he clenched his fists at the crowd, was the celebration of a man who knows the dream of a record-extending 57th Gibson Cup is still well and truly alive after a big win over their rivals.