Chelsea will spend the next few weeks considering their options in the winter transfer window before determining whether to target a striker amid growing concerns over Diego Costa.

Costa, such an integral figure in the team who won Chelsea’s first Premier League title for five years in May, has cut an increasingly agitated figure over recent weeks. The 27-year-old’s relationship with José Mourinho has been extremely strong – most notably over the two costly retrospective bans incurred by the forward since February – but it is showing signs of fracture. This despite public insistences to the contrary, with the pair embroiled in an ugly disagreement as the teams left the pitch at half-time in Tuesday’s comfortable 4-0 win against Maccabi Tel Aviv.

Mourinho, just as he did after a similar situation against Norwich on Saturday, made his frustrations clear at the forward’s lack of anticipation over an Eden Hazard pass, which would have provided the striker with a tap-in had he been on the move. Costa returned his manager’s remonstrations in kind. Oscar and John Terry tried to calm him down only to be pushed aside. The manager subsequently suggested there had been “a few kisses, a few cuddles” in the dressing room at the interval, and “no problem”, though the public show of dissent was notable.

Chelsea, 15th in the Premier League, would be loth to enter the transfer market in January, when pedigree players are generally unavailable. It is unlikely, for example, the long-coveted Antoine Griezmann could be secured from Atlético Madrid or Gonzalo Higuaín, whom the manager may prefer, from Napoli. Mourinho has admitted he has “no right” to ask the board for funds and said he would be happy to end the season with a squad largely unaltered from that which claimed the title.

Yet there remains a need to qualify for next season’s Champions League, with a top-four finish still considered the bare minimum requirement even in the wake of the club’s worst start under Roman Abramovich’s ownership. Given Costa has managed only seven goals in 10 months – there have been four in 17 games this season – the need for striker reinforcements is clear, with Radamel Falcao having proved ineffective over his loan spell from Monaco and Loïc Rémy reduced to a bit-part role often spent on the flank. Furthermore, Rémy’s wife is due to give birth, which may rule him out of Sunday’s trip to Tottenham.

The recruitment department, under the stewardship of the technical director, Michael Emenalo, would prefer to promote a long-term view if there is to be a push for new players, and have asked to be kept abreast of Saido Berahino’s potential availability at West Bromwich Albion. The England Under-21 forward had agitated for a move to Tottenham in August, with Spurs’ hopes of reviving that deal in the near future surely wrecked by the antipathy between the clubs’ respective chairmen, Jeremy Peace and Daniel Levy. Leicester’s prolific Jamie Vardy is, like Berahino, contracted through to 2017 but the league leaders would resist any attempt to prise him away mid-campaign.

Neither of those forwards is likely to fit the profile Mourinho would prefer and the manager could, instead, push for a short-term fix to bolster numbers for the remainder of the season before more established targets are pursued in the summer.

To that end, Emmanuel Adebayor’s availability as a free agent makes him an option, with the Togo forward having worked under Mourinho at Real Madrid, while Robin van Persie has failed to settle in Istanbul since moving to Fenerbahce this year and could be made available on loan.

Board and manager will liaise over the next few weeks, with Mourinho effectively reliant on Costa for the team’s forthcoming games given the lack of experienced options – the club have a number of young forwards out on loan, but none is deemed ready for the first team – elsewhere in his squad.

Although Costa, who scored 20 goals over his first season in Englandbut only three over the last four months of the season, played the whole of the second half in Haifa, his body language at half-time had been that of someone who no longer wanted to be on the pitch. He was already edging towards the tunnel while Predrag Rajkovic underwent treatment in stoppage time, and strode off immediately on the referee’s whistle without acknowledging his manager, who was standing on the touchline.

Gary Cahill is waiting to see whether he is offered new terms before his 30th birthday in mid-December. The centre-half’s deal expires in 2017 but Chelsea have a strict policy of offering only 12-month extensions to players who have entered their 30s. Branislav Ivanovic, 31, has yet to discover whether he will earn a one-year deal when his contract expires next summer.